Question

Evaluate:


(i) (62 +82)^1/2
​

Answer 1

⇒ $\sf\\ (62+82)^{\frac{1}{2}}$

⇒ $\sf (144)^{\frac{1}{2}}$

⇒ $\sf \sqrt{144}$

To find the square root we need to follow the steps below.

Step 1: Prime Factorize the number to obtain the product of primes.

$\begin{array}{r | l} 2 & 144 \\ \cline{2-2} 2 & 72 \\ \cline{2-2} 2 & 36 \\ \cline{2-2} 2&18 \\\cline{2-2} 3&9 \\\cline{2-2} &3 \\ \end{array}$

$\sf \bf \therefore\ 144 = 2\times 2 \times 2\times 2 \times 3\times 3$

Step 2: Pair the product of primes.

$\sf 144 = (2\times 2) \times (2\times 2) \times (3\times 3)$

Step 3: Take one number from each pair and multiply them to obtain the square root.

⇒ $\sf \sqrt{144} = 2 \times 2\times 3$

⇒ $\sf \sqrt{144}=12$

$\sf \bf \therefore (62+82)^{\frac{1}{2}}=12$

Additional Information

Exponents tell us how many times a number should be multiplied to itself.

For example⇒ 8²

Here the exponent is "2" and thus we need to multiply 8 two times to itself.

So 8² = 8×8 = 64

Exponents are also known as powers.

When the exponent is 2 we call it as square.

For example ⇒ 4²

We can pronounce this as 4 square or 4 raised to the power 2.

When the exponent is 3 we call it cube.

For example ⇒ 3³

We can pronounce this as 3 cube or 3 raised to the power 3.

Answer 2

$\boxed{\boxed{\boxed{\huge{\red{\mathfrak{hello}}}}}}$

${(62 + 82)}^{ \frac{1}{2} } \\ {144}^{ \frac{1}{2} }$

i.e,

$\sqrt{144} \\ = 12$

${\bold{\blue{\text{Hope It Is Helpful To U Dear}}}}$

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