Question

How do you simplify the square root of $T$ to the $17th$ power?

Answer 1

Hint: When we square a number the index or the exponent or the power of that number is multiplied by a factor of $2$. Here we are raising our number which in this case is given as $T$ by the power of $17$ which means the existing power of the given number will be multiplied by the value of $17$. Also remember that when we find the square root of any given number the value of the given number’s power is divided by $2$ or if we want to say in simple terms it is multiplied by $\dfrac{1}{2}$. We will therefore have to keep these two factors in our mind while solving such questions where we have to give the final power of the given number. The given number will be solved by multiplying and dividing the relevant numbers according to the powers that they are raised.

Formula used: $\sqrt{a}=a^{\dfrac{1}{2}}$

Complete step by step solution:
The given number is $T$ it is first given the square root which will make its power equal to ${T^{\dfrac{1}{2}}}$ because we know when we find out the square we multiply the power by $\dfrac{1}{2}$. Then we solve the $17th$ power. For that we write
$\sqrt{T^17}$
$\Rightarrow {T^{\dfrac{1}{2} \times 17}}$
Upon solving this further we get,
${T^8} \times {T^{\dfrac{1}{2}}}$
Thus we can finally write our expression as:
${T^8}\sqrt T $
Therefore, the square root of $T$ to the $17th$ power is ${T^8}\sqrt T $.

Note: While solving such a type of question in indices we should always remember that the powers or the roots value are always multiplied/divided to the existing power addition or subtraction of the power would yield us the wrong answer.