Pre-Algebra Examples

$\sqrt{144 y^{2} - 120 y + 25}$

Step 1

Factor using the perfect square rule.

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Step 1.1

Rewrite $144 y^{2}$ as ${(12 y)}^{2}$ .

$\sqrt{{(12 y)}^{2} - 120 y + 25}$

Step 1.2

Rewrite $25$ as $5^{2}$ .

$\sqrt{{(12 y)}^{2} - 120 y + 5^{2}}$

Step 1.3

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$120 y = 2 \cdot (12 y) \cdot 5$

Step 1.4

Rewrite the polynomial.

$\sqrt{{(12 y)}^{2} - 2 \cdot (12 y) \cdot 5 + 5^{2}}$

Step 1.5

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = 12 y$ and $b = 5$ .

$\sqrt{{(12 y - 5)}^{2}}$

Step 2

Pull terms out from under the radical, assuming positive real numbers.

$12 y - 5$