1. Tính: $\left[\sqrt{12} 3\sqrt{15}-4\sqrt{135}\right]\cdot\sqrt{3}$ $\sqrt{252}-\sqrt{700} \sqrt{1008}-\sqrt{448}$ \(2\sqrt{40\cdot\sqrt{12}}-2\sqrt{\sqrt{75}}-3\sqrt{5\sqr...

Câu 1: Thực hiện phép tính $a,\left(\sqrt{12}+3\sqrt{15}-4\sqrt{135}\right)\cdot\sqrt{3}\\ b,\sqrt{252}-\sqrt{700}+\sqrt{1008}-\sqrt{448}\\ c,2\sqrt{40\sqrt{12}}-2\sqrt{\sqrt{75}}-3\sqrt{5\sqrt{48}}$ Câu 2: Rút gọn $a,\frac{9\sqrt{5}+3\sqrt{27}}{\sqrt{5}+\sqrt{3}}\\ b,\frac{3\sqrt{8}+2\sqrt{12}+\sqrt{20}}{3\sqrt{18}-2\sqrt{27}+\sqrt{45}}\\ c,\left(4+\sqrt{15}\right)\cdot\left(\sqrt{10}-\sqrt{6}\right)\cdot\sqrt{4-\sqrt{15}}$ Câu 3:So...

0

ND

Nguyễn Dương

9 tháng 7 2019

0

NN

nguyễn ngọc trang

12 tháng 7 2018

a)($\sqrt{12}+3\sqrt{15}-4\sqrt{135}$) . $\sqrt{3}$

b) $\left(\sqrt{252}-\sqrt{700}+\sqrt{1008}-\sqrt{448}\right)$

2

DD

Duy Đỗ Ngọc Tuấn

12 tháng 7 2018

$\left(\sqrt{12}+3\sqrt{15}-4\sqrt{135}\right)\sqrt{3}$

$=\left(2\sqrt{3}+3\sqrt{15}-12\sqrt{15}\right)\sqrt{3}$

$=\left(2\sqrt{3}-9\sqrt{15}\right)\sqrt{3}$

$=6-9\sqrt{45}$

PK

Phùng Khánh Linh

12 tháng 7 2018

$a.\left(\sqrt{12}+3\sqrt{15}-4\sqrt{135}\right)\sqrt{3}=\left(2\sqrt{3}+3\sqrt{15}-12\sqrt{15}\right)\sqrt{3}=2.3-9\sqrt{9.5}=6-27\sqrt{5}$ $b.\sqrt{252}-\sqrt{700}+\sqrt{1008}-\sqrt{448}=\sqrt{36.7}-\sqrt{100.7}+\sqrt{144.7}-\sqrt{64.7}=6\sqrt{7}-10\sqrt{7}+12\sqrt{7}-8\sqrt{7}=0$

TínhA=$\left(4+\sqrt{15}\right)\left(\sqrt{10}-\sqrt{6}\right)\cdot\sqrt{4-\sqrt{15}}$B=$\left(3-\sqrt{5}\right)\cdot\sqrt{3+\sqrt{5}}+\left(3+\sqrt{5}\right)\cdot\sqrt{3-\sqrt{5}}$C=\(\sqrt{2+\sqrt{3}}\cdot\sqrt{2+\sqrt{2+\sqrt{3}}}\cdot\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{3}}}}\cdot\sqrt{2-\sqrt{2+\sqrt{2+\sqrt{...

AQ

Ác Quỷ Bóng Đêm

7 tháng 9 2016

1

NL

Nguyễn Lê Phước Thịnh

2 tháng 2 2022

a: $A=\left(4+\sqrt{15}\right)\cdot\left(\sqrt{5}-\sqrt{3}\right)\cdot\sqrt{8-2\sqrt{15}}$

$=\left(4+\sqrt{15}\right)\left(8-2\sqrt{15}\right)$

$=32-8\sqrt{15}+8\sqrt{15}-30=2$

b: $\sqrt{2}\cdot B=\left(3-\sqrt{5}\right)\left(\sqrt{5}+1\right)+\left(3+\sqrt{5}\right)\left(\sqrt{5}-1\right)$

$\Leftrightarrow B\sqrt{2}=3\sqrt{5}+3-5-\sqrt{5}+3\sqrt{5}-3+5-\sqrt{5}$

$\Leftrightarrow B\sqrt{2}=4\sqrt{5}$

hay $B=2\sqrt{10}$

d: $D\sqrt{2}=\sqrt{5}+\sqrt{3}+\sqrt{5}-\sqrt{3}-2\cdot\left(\sqrt{5}-1\right)$

$=2\sqrt{5}-2\sqrt{5}+2=2$

hay $D=\sqrt{2}$

LV

Lê Vũ Long Lê

14 tháng 5 2018

tính

$a.\sqrt{0,45.0,36}$

b.$\dfrac{\sqrt{405}+3\sqrt{27}}{3\sqrt[]{3}+45}$

c.$\sqrt{252}-\sqrt{700}+\sqrt{1008}-\sqrt{448}$

d.$\left(\sqrt{12}-2\sqrt{75}\right)\sqrt{3}$

7

MD

Mưa đầu mùa[ Do you know me ]

14 tháng 5 2018

ok chứ Long Lê

MD

Mưa đầu mùa[ Do you know me ]

14 tháng 5 2018

c. $\sqrt252-\sqrt700+\sqrt1008-\sqrt448$

$=6\sqrt{7}-10\sqrt{7}+12\sqrt{7}-8\sqrt{7}$

=(6-10+12-8)$\sqrt{7}$

=0

TP

Triết Phan

24 tháng 9 2021

Bài 1: Thực hiện phép tính :

a,$\sqrt{252}-\sqrt{700}+\sqrt{1008}-\sqrt{448}$

b,$\left(\sqrt{125}+\sqrt{245}-\sqrt{5}\right):\sqrt{5}$

c,$\left(2\sqrt{18}-5\sqrt{32}+6\sqrt{2}\right):\sqrt{2}$

1

NL

Nguyễn Lê Phước Thịnh

24 tháng 9 2021

a: Ta có: $\sqrt{252}-\sqrt{700}+\sqrt{1008}-\sqrt{448}$

$=6\sqrt{7}-10\sqrt{7}+12\sqrt{7}-8\sqrt{7}$

$=0$

b: Ta có: $\left(\sqrt{125}+\sqrt{245}-\sqrt{5}\right):\sqrt{5}$

$=5+7-1$

=11

Đúng(1)

AV

Ánh Vy HN

9 tháng 7 2019

2.

a,$\sqrt{12}-\sqrt{27}+\sqrt{3}$

b,$\sqrt{252}-\sqrt{700}+\sqrt{1008}-\sqrt{448};\sqrt{3}.\left(\sqrt{12}+\sqrt{27}-\sqrt{3}\right)$

c,$\frac{\sqrt{6}+\sqrt{10}}{\sqrt{21}+\sqrt{35}};\frac{\sqrt{405}+3\sqrt{27}}{3\sqrt{3}+\sqrt{45}}$

d,$\frac{\sqrt{2}+\sqrt{3}+\sqrt{4}-\sqrt{6}-\sqrt{9}-\sqrt{12}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}$

2

AH

Akai Haruma

Giáo viên

30 tháng 8 2019

a)

$\sqrt{12}-\sqrt{27}+\sqrt{3}=\sqrt{4}.\sqrt{3}-\sqrt{9}.\sqrt{3}+\sqrt{3}=2\sqrt{3}-3\sqrt{3}+\sqrt{3}$

$=\sqrt{3}(2-3+1)=0$

b)

$\sqrt{252}-\sqrt{700}+\sqrt{1008}-\sqrt{448}=\sqrt{4}.\sqrt{63}-\sqrt{4}.\sqrt{175}+\sqrt{4}.\sqrt{252}-\sqrt{4}.\sqrt{112}$

$=2(\sqrt{63}-\sqrt{175}+\sqrt{252}-\sqrt{112})$

$=2(\sqrt{9}.\sqrt{7}-\sqrt{25}.\sqrt{7}+\sqrt{36}.\sqrt{7}-\sqrt{16}.\sqrt{7})$

$=2(3\sqrt{7}-5\sqrt{7}+6\sqrt{7}-4\sqrt{7})=2\sqrt{7}(3-5+6-4)=0$

------------------

$\sqrt{3}(\sqrt{12}+\sqrt{27}-\sqrt{3})=\sqrt{36}+\sqrt{81}-\sqrt{9}$

$=\sqrt{6^2}+\sqrt{9^2}-\sqrt{3^2}=6+9-3=12$

AH

Akai Haruma

Giáo viên

30 tháng 8 2019

c)

$\frac{\sqrt{6}+\sqrt{10}}{\sqrt{21}+\sqrt{35}}=\frac{\sqrt{2}.\sqrt{3}+\sqrt{2}.\sqrt{5}}{\sqrt{7}.\sqrt{3}+\sqrt{7}.\sqrt{5}}=\frac{\sqrt{2}(\sqrt{3}+\sqrt{5})}{\sqrt{7}(\sqrt{3}+\sqrt{5})}=\frac{\sqrt{2}}{\sqrt{7}}$

$\frac{\sqrt{405}+3\sqrt{27}}{3\sqrt{3}+\sqrt{45}}=\frac{\sqrt{81}.\sqrt{5}+3\sqrt{9}.\sqrt{3}}{3\sqrt{3}+\sqrt{9}.\sqrt{5}}=\frac{9\sqrt{5}+9\sqrt{3}}{3\sqrt{3}+3\sqrt{5}}$

$=\frac{3(3\sqrt{5}+3\sqrt{3})}{3\sqrt{3}+3\sqrt{5}}=3$

d)

$\frac{\sqrt{2}+\sqrt{3}+\sqrt{4}-\sqrt{6}-\sqrt{9}-\sqrt{12}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}=\frac{\sqrt{2}+\sqrt{3}+\sqrt{4}-(\sqrt{6}+\sqrt{9}+\sqrt{12})}{\sqrt{2}+\sqrt{3}+\sqrt{4}}$

$=\frac{\sqrt{2}+\sqrt{3}+\sqrt{4}-(\sqrt{2}.\sqrt{3}+\sqrt{3}.\sqrt{3}+\sqrt{3}.\sqrt{4})}{\sqrt{2}+\sqrt{3}+\sqrt{4}}$

$=\frac{\sqrt{2}+\sqrt{3}+\sqrt{4}-\sqrt{3}(\sqrt{2}+\sqrt{3}+\sqrt{4})}{\sqrt{2}+\sqrt{3}+\sqrt{4}}=\frac{(\sqrt{2}+\sqrt{3}+\sqrt{4})(1-\sqrt{3})}{\sqrt{2}+\sqrt{3}+\sqrt{4}}=1-\sqrt{3}$

TÍNH :$A=\sqrt{3+\sqrt{5+2\sqrt{3}}}\cdot\sqrt{3-\sqrt{5+2\sqrt{3}}}$$B=\sqrt{4+\sqrt{8}}\cdot\sqrt{2+\sqrt{2+\sqrt{2}}}\cdot\sqrt{2-\sqrt{2+\sqrt{2}}}$$C=\sqrt{2+\sqrt{3}}\cdot\sqrt{2+\sqrt{2+\sqrt{3}}}\cdot\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{3}}}}\cdot\sqrt{2-\sqrt{2+\sqrt{2+\sqrt{3}}}}$$D=\left[4+\sqrt{15}\right]\left[\sqrt{10}-\sqrt{6}\right]\cdot\sqrt{4-\sqrt{15}}$\(E=\left[3-\sqrt{5}\right]\cdot\sqrt{3+\sqrt{5}}\text{...

LH

Luyện Hoàng Hương Thảo

15 tháng 7 2016

2

HL

Hoàng Lê Bảo Ngọc

15 tháng 7 2016

$A=\sqrt{3+\sqrt{5+2\sqrt{3}}.\sqrt{3-\sqrt{5+2\sqrt{3}}}}=\sqrt{\left(3^2\right)-\left(\sqrt{5+2\sqrt{3}}\right)^2}$

$=\sqrt{4-2\sqrt{3}}=\sqrt{\left(\sqrt{3}-1\right)^2}=\sqrt{3}-1$

$B=\sqrt{4+\sqrt{8}}.\sqrt{2+\sqrt{2+\sqrt{2}}}.\sqrt{2-\sqrt{2+\sqrt{2}}}$

$=\sqrt{4+2\sqrt{2}}.\sqrt{2^2-2-\sqrt{2}}=\sqrt{2}.\sqrt{2+\sqrt{2}}.\sqrt{2-\sqrt{2}}$

$=\sqrt{2}.\sqrt{4-2}=\sqrt{2}.\sqrt{2}=2$

$C=\sqrt{2+\sqrt{3}}.\sqrt{2+\sqrt{2+\sqrt{3}}}.\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{3}}}}.\sqrt{2-\sqrt{2+\sqrt{2+\sqrt{3}}}}$

$=\sqrt{2+\sqrt{3}}.\sqrt{2+\sqrt{2+\sqrt{3}}}.\sqrt{2^2-\left(2+\sqrt{2+\sqrt{3}}\right)}$

$=\sqrt{2+\sqrt{3}}.\sqrt{2+\sqrt{2+\sqrt{3}}}.\sqrt{2-\sqrt{2+\sqrt{3}}}=\sqrt{2+\sqrt{3}}.\sqrt{2^2-\left(2+\sqrt{3}\right)}$

$=\sqrt{2+\sqrt{3}}.\sqrt{2-\sqrt{3}}=\sqrt{4-3}=1$

HL

Hoàng Lê Bảo Ngọc

15 tháng 7 2016

$D=\left(4+\sqrt{15}\right)\left(\sqrt{10}-\sqrt{6}\right)\sqrt{4-\sqrt{15}}$

$=\sqrt{4+\sqrt{15}}.\sqrt{2}.\left(\sqrt{5}-\sqrt{3}\right).\sqrt{4+\sqrt{15}}.\sqrt{4-\sqrt{15}}$

$=\sqrt{\left(\sqrt{5}+\sqrt{3}\right)^2}.\left(\sqrt{5}-\sqrt{3}\right).\sqrt{4^2-15}$

$=\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5}-\sqrt{3}\right)=5-3=2$

$E=\left(3-\sqrt{5}\right)\sqrt{3+\sqrt{5}}+\left(3+\sqrt{5}\right).\sqrt{3-\sqrt{5}}$

$=\sqrt{3+\sqrt{5}}.\sqrt{3-\sqrt{5}}.\sqrt{3-\sqrt{5}}+\sqrt{3+\sqrt{5}}.\sqrt{3-\sqrt{5}}.\sqrt{3+\sqrt{5}}$

$=2\sqrt{3-\sqrt{5}}+2\sqrt{3+\sqrt{5}}=\sqrt{2}\left(\sqrt{6-2\sqrt{5}}+\sqrt{6+2\sqrt{5}}\right)$

$=\sqrt{2}.\left(\sqrt{5}-1+\sqrt{5}+1\right)=2\sqrt{10}$

HT

hoàng thiên

10 tháng 6 2019

1.Thực hiện phép tính:

a.$\sqrt{12}-\sqrt{27}+\sqrt{3}$

b.$\left(\sqrt{12}-2\sqrt{75}\right)\sqrt{3}$

c.$\sqrt{225}-\sqrt{700}+\sqrt{1008}-\sqrt{448}$

d.$\sqrt{3}\left(\sqrt{12}+\sqrt{27}-\sqrt{3}\right)$

1

HT

Hoàng Tử Hà

10 tháng 6 2019

Bấm máy tính là ra thui mà bn

a/ $=2\sqrt{3}-3\sqrt{3}+\sqrt{3}=0$

b/ $=\left(2\sqrt{3}-10\sqrt{3}\right)\sqrt{3}=-24$

c/ $=15-10\sqrt{7}+12\sqrt{7}-8\sqrt{7}=15-6\sqrt{7}$

d/ $=\sqrt{3}\left(2\sqrt{3}+3\sqrt{3}-\sqrt{3}\right)=12$

DD

Đinh Đức Thắng

6 tháng 8 2019

Thực hiện các phép tính sau:

a, $\left(\sqrt{6}+\sqrt{2}\right)\cdot\left(\sqrt{3}-2\right)\cdot\sqrt{\sqrt{3}+2}$

b, $\left(4+\sqrt{15}\right)\cdot\left(\sqrt{10}-\sqrt{6}\right)\cdot\sqrt{4-\sqrt{15}}$

c, $\sqrt{13-\sqrt{160}}-\sqrt{53+4\sqrt{90}}$

d, $\sqrt{6-2\sqrt{\sqrt{2}+\sqrt{12}+\sqrt{18-\sqrt{128}}}}$