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9 grade maths> how can you write x = 7 +40 1/2 as (____)...

question mark

how can you write x = 7 +401/2 as (____)2. please explain.

Rahul Jiji George , 10 Years ago

Grade 10

2 Answers

SHAIK AASIF AHAMED

Last Activity: 10 Years ago

Hello student,
Please find the answer to your question below
As we know that
(a+b)²=a²+2ab+b²
Similarly ( $\sqrt{a}$ + $\sqrt{b}$ )²=a+b+2 $\sqrt{a}$ $\sqrt{b}$ …..............(1)
given 7+ [sqrt{40}] =2+5+ [sqrt{40}]
as [ $\sqrt{40}$ ] = $\sqrt{10*4}$ =2 $\sqrt{10}$
we get 7+ [ $\sqrt{40}$ ] =2+5+2 [ $\sqrt{10}$ ] =( $\sqrt{2}$ )²+( $\sqrt{5}$ )²+2 $\sqrt{5}$ $\sqrt{2}$ =( $\sqrt{2}$ + $\sqrt{5}$ )²
from property (1)
I hope its clear now

Sumit Majumdar

Last Activity: 10 Years ago

Dear student,
We can have:
$x=7+40^{\frac{1}{2}}=7+2(10)^{\frac{1}{2}}=2+5+2\sqrt{2}\sqrt{5}=(\sqrt{2})^2+(\sqrt{5})^2+2\sqrt{2}\sqrt{5}=\left ( \sqrt{2}+\sqrt{5} \right )^2$ Regards

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