Question

Evaluate : `root(3)(4+root(3)(61+root(3)(27)))​

Answer 1

3√61+3√25+3√8 ​ = 47.298

The given expression is :

3√61+3√25+3√8 .

We need to break the given square roots into smaller roots.

As 61 = 3*3*7

So, √61 = √(3*3*7) = 3√7

Again, √25 = 5

And, √8 = √(2*2*2) = 2√2

Replacing these in the main expression, we get,

3[3√7] + 3(5) + 3[2√2]

= 9√7 + 15 + 6√2

As the value of √7 = 2.646 and √2 = 1.414. So,

= 9(2.646) + 15 + 6(1.414)

= 47.298