Square Roots: Practice

A square root asks what non-negative number squared gives the radicand.

$3^2 = 9 \quad\Rightarrow\quad \sqrt{9} = 3$

It is not $9 \div 2 = 4.5$, and it is not $9^2 = 81$.

Find the non-negative number that squares to $16$.

$4^2 = 16 \quad\Rightarrow\quad \sqrt{16} = 4$

It is not $16 \div 2 = 8$.

Look for the non-negative number whose square is $1$.

$1^2 = 1 \quad\Rightarrow\quad \sqrt{1} = 1$

One is its own square, so its square root is $1$.

Find the non-negative number that squares to $49$.

$7^2 = 49 \quad\Rightarrow\quad \sqrt{49} = 7$

Ask which number squared gives $0$.

$0^2 = 0 \quad\Rightarrow\quad \sqrt{0} = 0$

Zero is the one radicand whose root needs no choice of sign.

Find the non-negative number whose square is $100$.

$10^2 = 100 \quad\Rightarrow\quad \sqrt{100} = 10$

Find the non-negative number that squares to $4$.

$2^2 = 4 \quad\Rightarrow\quad \sqrt{4} = 2$

Squaring and taking the square root are inverse operations, so squaring $8$ undoes the root and returns the radicand.

$8^2 = 64$

That is exactly the number whose square root was $8$.

Find the non-negative number whose square is $144$.

$12^2 = 144 \quad\Rightarrow\quad \sqrt{144} = 12$

Find the non-negative number that squares to $81$.

$9^2 = 81 \quad\Rightarrow\quad \sqrt{81} = 9$

Find the non-negative number whose square is $121$.

$11^2 = 121 \quad\Rightarrow\quad \sqrt{121} = 11$

Find the non-negative number that squares to $64$.

$8^2 = 64 \quad\Rightarrow\quad \sqrt{64} = 8$