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how can you write x = 7 +40 1/2 as (____) 2 . please explain.

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

Grade:10

2 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
6 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 IIT Delhi
askIITians Faculty 137 Points
6 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 )^2Regards

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