Respuesta :
Answer:
to solve that it gonna be 10 square root of 2 and in decimal form it gonna be 14.14213562
Hope this helps
Step-by-step explanation:
Answer: 200
=====================================
Work Shown:
One approach is to simplify the stuff under the second power exponent. After that simplification, you would then square the result.
[tex]x = \sqrt{2}+\sqrt{8}+\sqrt{18}+\sqrt{32}\\\\x = \sqrt{2}+\sqrt{4*2}+\sqrt{9*2}+\sqrt{16*2}\\\\x = \sqrt{2}+\sqrt{4}*\sqrt{2}+\sqrt{9}*\sqrt{2}+\sqrt{16}*\sqrt{2}\\\\x = 1\sqrt{2}+2\sqrt{2}+3\sqrt{2}+4\sqrt{2}\\\\x = (1+2+3+4)\sqrt{2}\\\\x = 10\sqrt{2}\\\\x^2 = \left(10\sqrt{2}\right)^2\\\\x^2 = \left(10\sqrt{2}\right)*\left(10\sqrt{2}\right)\\\\x^2 = 10*10\sqrt{2}*\sqrt{2}\\\\x^2 = 100\sqrt{2*2}\\\\x^2 = 100\sqrt{4}\\\\x^2 = 100*2\\\\x^2 = 200\\\\[/tex]
So,
[tex]\left(\sqrt{2}+\sqrt{8}+\sqrt{18}+\sqrt{32}\right)^2 = 200[/tex]
-----------------------------------------------------
Checking the answer:
Using a calculator,
sqrt(2)+sqrt(8)+sqrt(18)+sqrt(32) = 14.142135623731
Then you square that to get (14.142135623731)^2 = 200.000000000001
Your calculator may not have that 1 at the end. It shouldn't be there and it's a result of rounding error. But it's close enough to 200.
