Simplify the following: √27, √50, √72, √48, √45, √120, √130, √112, √52, √300

Question

ScanSolve AI Tutor · Accepted Answer

Here are the simplified forms of the square roots:

1. $\sqrt{27}$

\sqrt{27} = \sqrt{9 \times 3}

= \sqrt{9} \times \sqrt{3}

= 3 \times \sqrt{3}

= \boxed{3\sqrt{3}}

2. $\sqrt{50}$

\sqrt{50} = \sqrt{25 \times 2}

= \sqrt{25} \times \sqrt{2}

= 5 \times \sqrt{2}

= \boxed{5\sqrt{2}}

3. $\sqrt{72}$
The student's work reached $3\sqrt{8}$ .

Factor out the largest perfect square from 8.
$3\sqrt{8} = 3\sqrt{4 \times 2}$
Apply the product rule for square roots.
$3\sqrt{4 \times 2} = 3 \times \sqrt{4} \times \sqrt{2}$
Simplify the perfect square and multiply.
$3 \times 2 \times \sqrt{2} = \boxed{6\sqrt{2}}$
4. $\sqrt{48}$
Factor out the largest perfect square from 48.
$\sqrt{48} = \sqrt{16 \times 3}$
Apply the product rule for square roots.
$\sqrt{16 \times 3} = \sqrt{16} \times \sqrt{3}$
Simplify the perfect square.
$\sqrt{16} \times \sqrt{3} = \boxed{4\sqrt{3}}$
5. $\sqrt{45}$
$\sqrt{45} = \sqrt{9 \times 5}$ $= \sqrt{9} \times \sqrt{5}$ $= 3 \times \sqrt{5}$ $= \boxed{3\sqrt{5}}$
6. $\sqrt{120}$
Factor out the largest perfect square from 120.
$\sqrt{120} = \sqrt{4 \times 30}$
Apply the product rule for square roots.
$\sqrt{4 \times 30} = \sqrt{4} \times \sqrt{30}$
Simplify the perfect square.
$\sqrt{4} \times \sqrt{30} = \boxed{2\sqrt{30}}$
7. $\sqrt{130}$
Identify perfect square factors of 130.
The factors of 130 are 1, 2, 5, 10, 13, 26, 65, 130. The only perfect square factor is 1.
Therefore, $\sqrt{130}$ cannot be simplified further.
$\boxed{\sqrt{130}}$
8. $\sqrt{112}$
Factor out the largest perfect square from 112.
$\sqrt{112} = \sqrt{16 \times 7}$
Apply the product rule for square roots.
$\sqrt{16 \times 7} = \sqrt{16} \times \sqrt{7}$
Simplify the perfect square.
$\sqrt{16} \times \sqrt{7} = \boxed{4\sqrt{7}}$
9. $\sqrt{52}$
Factor out the largest perfect square from 52.
$\sqrt{52} = \sqrt{4 \times 13}$
Apply the product rule for square roots.
$\sqrt{4 \times 13} = \sqrt{4} \times \sqrt{13}$
Simplify the perfect square.
$\sqrt{4} \times \sqrt{13} = \boxed{2\sqrt{13}}$
10. $\sqrt{300}$
Factor out the largest perfect square from 300.
$\sqrt{300} = \sqrt{100 \times 3}$
Apply the product rule for square roots.
$\sqrt{100 \times 3} = \sqrt{100} \times \sqrt{3}$
Simplify the perfect square.
$\sqrt{100} \times \sqrt{3} = \boxed{10\sqrt{3}}$

Simplify the following: √27, √50, √72, √48, √45, √120, √130, √112, √52, √300

Step-by-step solution

Factor out the largest perfect square from 8.

Apply the product rule for square roots.

Simplify the perfect square and multiply.

Factor out the largest perfect square from 48.

Apply the product rule for square roots.

Simplify the perfect square.

Factor out the largest perfect square from 120.

Apply the product rule for square roots.

Simplify the perfect square.

Identify perfect square factors of 130.

Factor out the largest perfect square from 112.

Apply the product rule for square roots.

Simplify the perfect square.

Factor out the largest perfect square from 52.

Apply the product rule for square roots.

Simplify the perfect square.

Factor out the largest perfect square from 300.

Apply the product rule for square roots.

Simplify the perfect square.

Still stuck on this one?

More Mathematics Questions