Evaluate the square root of 9 + 4√5 in the form c + √d

Question

asked Aug 5, 2024 159k views

1 Answer

Aaronaught · Answer 1 · 2024-08-09T17:15:27+0000

Explanation:

Here we are interested in finding the square root of
$9 +4\sqrt5$ . So , we have

$\longrightarrow √( 9+4\sqrt5)$

We can write it as ,

$\longrightarrow √( 5 + 4 + 4\sqrt5)$

This can be again rewritten as ,

$\longrightarrow√( (\sqrt5)^2+2^2+ 2(2)(\sqrt5) )$

Now this in the form of
a^2+b^2+2ab form which is the square of
(a+b) . So that,

$\longrightarrow √( (2+\sqrt5)^2)$

Simplify the root ,

$\longrightarrow 2 + \sqrt5$

Hence we got our answer in the form of
c +√(d)

And we are done!

—Rishabh