Question

Square root 6 multiplied by square root 8

Answer 1

$\sqrt{6}\times\sqrt{8}=4\sqrt{3}$

Concept :

If $a$ be a number, then we have the relation

$\quad\sqrt{a^{2}}=a$, which is obtained from

$\sqrt{a^{2}}=(a^{2})^{\frac{1}{2}}=a^{\frac{2}{2}}=a^{1}=a$.

Step-by-step explanation:

Now, $\sqrt{6}\times\sqrt{8}$

$=\sqrt{6\times 8}$

• Tip. $\sqrt{a}\times\sqrt{b}=\sqrt{a\times b}$ and this is obtained using the rule:

• $a^{m}\times b^{m}=(a\times b)^{m}$

$=\sqrt{2\times 3\times 2\times 2\times 2}$

• Tip. Here, we have prime factorized the numbers $6$ and $8$

• Now, rearrange the numbers.

$=\sqrt{2\times 2\times 2\times 2\times 3}$

$=\sqrt{2^{2}\times 2^{2}\times 3}$

$=2\times 2\times \sqrt{3}$

$=4\sqrt{3}$

Therefore, $\sqrt{6}\times\sqrt{8}=4\sqrt{3}$.