Question

Simplify whether root50 * root162 is surd or not surd

Answer 1

Answer:

It's a surd.

Step-by-step explanation:

On multiplying √50 and √162 you get the answer as √8000 and on finding the factors it comes out to be 40√5 which is a surd.

Answer 2

$\sqrt{50} \times \sqrt{162} \\ \\ = \sqrt{50 \times 162} \\ \\ = \sqrt{5 \times 5 \times 2 \times 2 \times 3 \times 3 \times 3 \times 3} \\ \\ = \sqrt{25 \times 4 \times 9 \times 9} \\ \\ = 5\sqrt{4 \times 9 \times 9} \\ \\ = (5 \times 2)\sqrt{9 \times 9} \\ \\ = 10 \sqrt{9 \times 9} \\ \\ = 10 \sqrt{81} \\ \\ = 10 \times 9 \\ \\ = \green{\boxed{90}}$

Hence, the value of √50 × √162 = 90 is a rational number therefore, √50 × √162 is not a surd.