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What is (square root of $ 3 $ ) to the power of $ 2 $ ?

Last updated date: 13th Jul 2024
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Hint: The power is used to express mathematical equations in the short form; it is an expression that represents the repeated multiplication of the same factor. For example - $ 2 \times 2 \times 2 $ can be expressed as $ {2^3} $ . Here, the number two is called the base and the exponent represents the number of times the base is used as the factor. First we will frame the mathematical expression from the given word statement.

Complete step-by-step answer:
Given word statement: (square root of $ 3 $ ) to the power of $ 2 $
Mathematical expression: $ {(\sqrt 3 )^2} $
The above expression can be re-written as –
 $ = {3^{\dfrac{1}{2} \times 2}} $
By the property of the Power rule: to raise Power to power you have to multiply the exponents such as $ {\left( {{x^a}} \right)^b} = {x^{ab}} $ .
 $ = {3^{\dfrac{2}{2}}} $
Common factors from the numerator and the denominator cancels each other. Therefore, remove from the numerator and the denominator.
 $ = 3 $
Hence, the required answer is (square root of $ 3 $ ) to the power of $ 2 $ is $ 3 $
So, the correct answer is “3”.

Note: Remember the seven basic rules of the exponent or the laws of exponents to solve these types of questions. Make sure to go through the below mention rules, it describes how to solve different types of exponents problems and how to add, subtract, multiply and divide the exponents.
I.Product of powers rule
II.Quotient of powers rule
III.Power of a power rule
IV.Power of a product rule
V.Power of a quotient rule
VI.Zero power rule