Question

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

Answer 1

Answer:

$20 i^{4} j^{2} k^{3}$

Step-by-step 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

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

Properties used:

$x^{m \times n}=(x^{m})^{n} \\\\\sqrt{x} =x^{\frac{1}{2} }$