Question

Evaluate :
Whole square root 13 + 4 root 10 - whole square root 7 minus 2 root 10

Answer 1

Answer:

$\sqrt{13+4\sqrt{10}}-\sqrt{7-2\sqrt{10}}=\sqrt{10}+1$

Step-by-step explanation:

Given : Expression Whole square root 13 + 4 root 10 - whole square root 7 minus 2 root 10.

To find : Evaluate the given expression?

Solution :

Expression $\sqrt{13+4\sqrt{10}}-\sqrt{7-2\sqrt{10}}$

Now, solving the expression

$\sqrt{13+4\sqrt{10}}-\sqrt{7-2\sqrt{10}}=0$

$\sqrt{13+4\sqrt{10}}=\sqrt{7-2\sqrt{10}}$

Squaring both side,

$(\sqrt{13+4\sqrt{10}})^2=(\sqrt{7-2\sqrt{10}})^2$

$13+4\sqrt{10}=7-2\sqrt{10}$

$4\sqrt{10}+2\sqrt{10}=7-13$

$6\sqrt{10}=-6$

$\sqrt{10}=-1$

Therefore, $\sqrt{13+4\sqrt{10}}-\sqrt{7-2\sqrt{10}}=\sqrt{10}+1$