Question

Is square root 2 ×square root 8 irrational ? Justify your answer

Answer 1

When two or more terms have same roots then we can simply multiply them.

Hence,

√ 2 * √ 8
√ ( 2 * 8 )

On prime factorizing the terms,

√ ( 2 * 2 * 2 * 2 )

Taking out pairs of the root,

2 * 2

4

Here our result is a rational number i.e. 4 which can be expressed in p / q form where q ≠ 0.

Hence,

√2 * √8 is also a rational number.

Answer 2

$\huge\bold\color {green}{Hello \: Friend \: !!}$


$\red {\bold {Here \: is \: your \: answer}}$


$\underline\bold {\red{Answer : No, It \: is \: rational}}$


$\bold {↪ \: \sqrt{a} \: \times \: \sqrt{b} \: = \: \sqrt{ab} }$


$\bold {↪ \sqrt{2} \: \times \: \sqrt{8} \: = \: \sqrt{2 \: \times \: 8} }$


$\bold {↪ \sqrt{2} \: \times \: \sqrt{8} \: = \: \sqrt{16} }$


$\bold {↪ \sqrt{2} \: \times \: \sqrt{8} \: = \: 4 }$


$\bold {↪ 4 \: is \: not \: an\: irrational \: number}$



$\mathbb {\huge {\fcolorbox{yellow}{green}{Hope It Helps}}}$