Question

Divide

$\sf \red{1.} \: 4 \sqrt{10} \: \: by \: \: 2 \sqrt{5}$
$\sf \red{2.} \: 12 \sqrt{38} \: \: by \: \: 3 \sqrt{7}$
$\sf \red{3.} \: 18 \sqrt{30} \: \: by \: \: 9 \sqrt{6}$
Class 9
Mathematics
Chapter 1 ( Number System )​ .

Answer 1

Step-by-step explanation:

Solutions:-

1)Given that 4√10 ÷ 2√5

It can be written as

=> 4√10/2√5

=>(2×2×√2×√5)/(2×√5)

=> 2×√2

=> 2√2

4√10 ÷ 2√5 = 2√2

2)Given that 12√38 ÷3√7

It can be written as

=> 12√38/3√7

=> (3×4×√38)/(3×√7)

=>(4×√38)/√7

=>4√38/√7

or

On Rationalising the denominator then

=> (4√38)×√7/(√7×√7)

=> (4×√38×√7)/(√7)²

=> 4×√(38×7)/7

=>4×√266/7

=> 4√266/7

12√38 ÷3√7 = 4√38/√7 or 4√266/7

3)Given that : 18√30 ÷ 9√6

It can be written as

=> 18√30 / 9√6

=> (18×√30)/(9×√6)

=> (2×9×√5×√6)/(9×√6)

=> 2×√5

=> 2√5

18√30 ÷ 9√6 = 2√5

Answer 2

Answer:

First, we have to know these :

$\odot\: \: \sqrt{xy} = \sqrt{x} \: \times \: \sqrt{y} \\ \odot \: \: x = \sqrt{x} \times \sqrt{x}$

Solution :

$\large \red{1)} \\ \frac{4 \sqrt{10} }{2 \sqrt{5} } \\ = \frac{2 \times 2 \times \sqrt{2 \times 5} }{2 \times \sqrt{5} } \\ = \frac{\cancel{2} \times 2 \times \sqrt{2 } \times \cancel{\sqrt{5} }}{ \cancel{2} \times \cancel{ \sqrt{5} } } \\ = 2 \sqrt{2}$

$\large \red{2)} \\ \frac{12 \sqrt{38} }{3 \sqrt{7} } \\ = \frac{\cancel{3 }\times 4 \times \sqrt{38} }{\cancel{3 }\times \sqrt{7} } \\ = \frac{4 \sqrt{38} }{ \sqrt{7} } \\ = \frac{4 \sqrt{38} \times \sqrt{7} }{ \sqrt{7} \times \sqrt{7} } \\ = \frac{4 \sqrt{38 \times 7} }{7} \\ = \frac{4 \sqrt{266} }{7}$

$\large \red{ 3)} \\ \frac{18 \sqrt{30} }{9 \sqrt{6} } \\ = \frac{9 \times 2 \times \sqrt{5 \times 6} }{9 \times \sqrt{6} } \\ = \frac{\cancel{9} \times 2 \times \sqrt{5} \times \cancel{\sqrt{6} }}{\cancel{9} \times \cancel{\sqrt{6} }} \\ = 2 \sqrt{5}$