Question

What is the value of $k$, if$\sqrt {10k + 3} = 5$?
A. $0.2$
B. $2$
C. $2.2$
D. $2.8$
E. $4.7$

Answer 1

Hint: Here we are given that $\sqrt {10k + 3} = 5$
So squaring both sides we will get that
$10k + 3 = {5^2}$
Now we can get the value required by simplifying and solving the above equation.

Complete step-by-step answer:
Here in this question we are given to find the variable $k$ out of the equation which is given as $\sqrt {10k + 3} = 5$ and here we are given the square root function and here the symbol $\sqrt {f(x)} $ denote the square root of the function $f(x)$
For example: If we are given to find the square root of the function $x$ then it will be denoted by the function $\sqrt x $ or it can also be written in the form of ${x^{\dfrac{1}{2}}}$ and hence we can say that $\sqrt x $$ = $${x^{\dfrac{1}{2}}}$ both are similar. If we are given the function like this $\sqrt[3]{x}$ then it can be also written as${x^{\dfrac{1}{3}}}$. So for solving the above equation first we need to remove the square root by squaring both the sides.
For example: If we are given that $x = 5$ then squaring both the sides will give us ${x^2} = 25$ that will be equal.
Similarly here we are given that
$\sqrt {10k + 3} = 5$
We can write it as
$\Rightarrow$ ${(10k + 3)^{\dfrac{1}{2}}} = 5$
Now squaring both the sides we will get that
$\Rightarrow$ ${(10k + 3)^{\dfrac{1}{2} \times 2}} = {5^2}$
So we get that
$\Rightarrow$ $10k + 3 = 25$
$
\Rightarrow 10k = 25 - 3 \\
\Rightarrow 10k = 22 \\
\Rightarrow k = \dfrac{{22}}{{10}} = 2.2 \\
 $
So $k = 2.2$ is the solution of our answer.

Note: If we are writing that $y = \sqrt {f(x)} $ then $f(x)$ cannot be negative. The function $f(x)$ must be greater than or equal to zero that means that the square root of the negative number is an imaginary number and not the real number. So function inside the root must be greater than or equal to zero.