Square Roots - Examples, Exercises and Solutions

What are those mysterious square roots that often confuse students and complicate their lives? The truth is that to understand them, we need to grasp the concept of the inverse operation.

What is a square root?

When we solve an exercise like $5=25^2$, it's clear that $5$ times $5$ (that is, multiplying the number by itself) results in $25$. This is the concept of a power, or to be more precise, a square power, which to apply, we must multiply the figure or the number by itself.

The concept of "square root" refers to the inverse operation of squaring numbers.

That is, if we have $X^2=25$ and we want to find the value of $X$, what we need to do is perform an identical operation on both sides of the equation.

This operation is the square root.

So, we have: $\sqrt{X^2} = \sqrt{25}$ and the result is $X=5$.

Examples with solutions for Square Roots

Exercise #1

Choose the largest value

Step-by-Step Solution

Let's calculate the numerical value of each of the roots in the given options:

$\sqrt{25}=5\\ \sqrt{16}=4\\ \sqrt{9}=3\\$and it's clear that:

5>4>3>1 Therefore, the correct answer is option A

$\sqrt{25}$

Exercise #2

$\sqrt{441}=$

Step-by-Step Solution

The root of 441 is 21.

$21\times21=$

$21\times20+21=$

$420+21=441$

$21$

Exercise #3

$(\sqrt{380.25}-\frac{1}{2})^2-11=$

Step-by-Step Solution

According to the order of operations, we'll first solve the expression in parentheses:

$(\sqrt{380.25}-\frac{1}{2})=(19.5-\frac{1}{2})=(19)$

In the next step, we'll solve the exponentiation, and finally subtract:

$(19)^2-11=(19\times19)-11=361-11=350$

350

Exercise #4

$\sqrt{64}=$

8

Exercise #5

$\sqrt{36}=$

6

Exercise #6

$\sqrt{49}=$

7

Exercise #7

$\sqrt{121}=$

11

Exercise #8

$\sqrt{100}=$

10

Exercise #9

$\sqrt{144}=$

12

Exercise #10

$\sqrt{x}=1$

1

Exercise #11

$\sqrt{36}=$

6

Exercise #12

$\sqrt{16}=$

4

Exercise #13

$\sqrt{x}=2$

4

Exercise #14

$\sqrt{9}=$

3

Exercise #15

$\sqrt{4}=$