Question

If a is a positive integer then √a√a√a√a√a√a=​

Answer 1

Answer:

Step-by-step explanation:

Answer:-

Given:-

• a is a positive integer.
• We need the value of :-

$\boxed{\sf{\sqrt{a} \times \sqrt{a} \times \sqrt{a} \times \sqrt{a} \times \sqrt{a} \times \sqrt{a}}}$

Trick:-

• Even number of times, we know that 2 times of square root a will give us a .

Let's Do!

$\sf{\underbrace{{\sqrt{a} \times \sqrt{a}} }_a \times \underbrace{{\sqrt{a} \times \sqrt{a}} }_a \times \underbrace{{\sqrt{a} \times \sqrt{a}} }_a}}$

$\sf{ \longrightarrow a \times a \times a}$

$\longrightarrow \sf{a^3}$ is the required answer.

Things to Note:-

• While attempting these questions, check the number of terms.
• Also, the square roots are considered in plus minus sign.
• In this, it was mentioned it is positive integer, hence it is positive.
• 2 times of any square root gives us the number in whole number.

Answer 2

★ ANSWER :

$\sqrt{a} \: \times \: \sqrt{a} \: \times \: \sqrt{a} \: \times \: \sqrt{a} \: \times \: \sqrt{a} \: \times \: \sqrt{a} = {a}^{3}$

Step-by-step explanation:

★ QUESTION :

If a is a positive integer then √a√a√a√a√a√a = ?

★ CONCEPT USED :

While finding the perfect square from square roots we need to take pairs of same square roots and multiply them and finally we get the perfect square.

★ SOLUTION :

$\sqrt{a} \: \times \: \sqrt{a} \: \times \: \sqrt{a} \: \times \: \sqrt{a} \: \times \: \sqrt{a} \: \times \: \sqrt{a} \\ \\ \: = \: \underline\bold{\sqrt{a} \: \times \: \: \sqrt{a}} \: \times \underline \bold{\sqrt{a} \: \times \: \sqrt{a}} \: \times \: \underline \bold{\sqrt{a} \: \times \: \sqrt{a} } \\ \\ = \: a \: \times \: a \: \times \: a \\ \\ = {a}^{3}$

★ ANSWER :

$\sqrt{a} \: \times \: \sqrt{a} \: \times \: \sqrt{a} \: \times \: \sqrt{a} \: \times \: \sqrt{a} \: \times \: \sqrt{a} = {a}^{3}$

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★ ALTERNATIVE METHOD

★ QUESTION :

If a is a positive integer then √a√a√a√a√a√a = ?

★ CONCEPT USED :

• $\sqrt[a]{x} \: = \: x ^{ \frac{1}{a} }$
• $\sqrt{a} \: = \: {a}^{ \frac{1}{2} }$
• ${a}^{x} \: \times \: {a}^{y} \: = {a}^{x \: + \: y}$
• ${a}^{x} \: \div \: {a}^{y} \: = \: {a}^{x \: - \: y}$

★ SOLUTION :

$\sqrt{a} \: \times \: \sqrt{a} \: \times \: \sqrt{a} \: \times \: \sqrt{a} \: \times \sqrt{a} \: \times \: \sqrt{a} \\ \\ = {a}^{ \frac{1}{2} } \: \times \: {a}^{ \frac{1}{2} } \: \times \: {a}^{ \frac{1}{2} } \: \times \: {a}^{ \frac{1}{2} } \: \times \: {a}^{ \frac{1}{2} } \: \times \: {a}^{ \frac{1}{2} } \\ \\ = \: {a}^{ \frac{1}{2} \: + \frac{1}{2} \: +\frac{1}{2} \: + \frac{1}{2} \: +\frac{1}{2} \: + \frac{1}{2} \: } \\ \\ = {a}^{ \frac{1}{2} \: \times \: 6} \\ \\ = {a}^{ \frac{1}{ \not2} \: \times \: \not6} \\ \\ = {a}^{3}$

★ ANSWER :

$\sqrt{a} \: \times \: \sqrt{a} \: \times \: \sqrt{a} \: \times \: \sqrt{a} \: \times \: \sqrt{a} \: \times \: \sqrt{a} = {a}^{3}$

HOPE IT HELPS YOU !

THANKS !