Question

Which expression is equivalent to √400 i^8 j^4 k^6

Answer 1

`20 i^(4) j^(2) k^(3)`

Explanation:

We have to simplify the following expression:

`\sqrt{400i^(8) j^(4) k^(6) }`

400 can be written as square of 20. The given expression can be simplified using the properties of exponents as shown below

`\sqrt{20^(2) i^(8) j^(4) k^(6) }\\\\ =\sqrt{(20)^(2)(i^(4) )^(2) (j^(2) )^(2) (k^(3) )^(2) } \\\\=\sqrt{(20 i^(4) j^(2) k^(3) )^(2) } \\\\ =((20 i^(4) j^(2) k^(3) )^(2))^{(1)/(2) }\\\\ =20 i^(4) j^(2) k^(3)`

Properties used:

`x^(m * n)=(x^(m))^(n) \\\\√(x) =x^{(1)/(2) }`