Let's calculate by performing each operation one step at a time:
Notice that the squaring the square root gives the number under the square root:
This result holds in general for any non-negative number. If is any positive number or zero, then
The square and the square root cancel each other out, and we're left with the number that we started with.
Find the value of
The number in the square root is non-negative, so the square and the square root cancel each other out.
Therefore, we have
Calculate $(\sqrt{324})^2.$
|
a
|
$-18$ |
|
b
|
$36$ |
|
c
|
$-324$ |
|
d
|
$324$ |
|
e
|
$18$ |
What is $(\sqrt{64})^2?$
|
a
|
$8$ |
|
b
|
$- 64$ |
|
c
|
$4$ |
|
d
|
$-8$ |
|
e
|
$64$ |
We must be careful when taking the square root of a negative number that's been squared.
For example, is not equal to We can write this using a not equal to symbol as
This is because the square root of a number can only be positive or zero, never negative. Let's work it out the long way:
So, we conclude that
For any positive perfect square, we always have exactly two numbers whose squares equal that number. Here, we have But by definition the square root is always positive (or zero) and cannot be negative. So here, and for any non-negative we get
Calculate the value of
Remember that by definition, the square root is always zero or positive, never negative.
So, the square root comes out to
What is $\sqrt{\left(-49\right)^2}?$
|
a
|
$7$ |
|
b
|
$\pm 49$ |
|
c
|
$49$ |
|
d
|
Not a real number |
|
e
|
$-7$ |
What is $\sqrt{\left(-25\right)^2}?$
|
a
|
Not a real number |
|
b
|
$25$ |
|
c
|
$\pm 25$ |
|
d
|
$-25$ |
|
e
|
$625$ |