Pre-Algebra Examples

$\sqrt{75 x^{2} + 30 x + 3}$

Step 1

Factor $3$ out of $75 x^{2} + 30 x + 3$ .

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Step 1.1

Factor $3$ out of $75 x^{2}$ .

$\sqrt{3 (25 x^{2}) + 30 x + 3}$

Step 1.2

Factor $3$ out of $30 x$ .

$\sqrt{3 (25 x^{2}) + 3 (10 x) + 3}$

Step 1.3

Factor $3$ out of $3$ .

$\sqrt{3 (25 x^{2}) + 3 (10 x) + 3 (1)}$

Step 1.4

Factor $3$ out of $3 (25 x^{2}) + 3 (10 x)$ .

$\sqrt{3 (25 x^{2} + 10 x) + 3 (1)}$

Step 1.5

Factor $3$ out of $3 (25 x^{2} + 10 x) + 3 (1)$ .

$\sqrt{3 (25 x^{2} + 10 x + 1)}$

Step 2

Factor using the perfect square rule.

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Step 2.1

Rewrite $25 x^{2}$ as ${(5 x)}^{2}$ .

$\sqrt{3 ({(5 x)}^{2} + 10 x + 1)}$

Step 2.2

Rewrite $1$ as $1^{2}$ .

$\sqrt{3 ({(5 x)}^{2} + 10 x + 1^{2})}$

Step 2.3

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

$10 x = 2 \cdot (5 x) \cdot 1$

Step 2.4

Rewrite the polynomial.

$\sqrt{3 ({(5 x)}^{2} + 2 \cdot (5 x) \cdot 1 + 1^{2})}$

Step 2.5

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = 5 x$ and $b = 1$ .

$\sqrt{3 {(5 x + 1)}^{2}}$

Step 3

Rewrite $3 {(5 x + 1)}^{2}$ as ${(5 x + 1^{2})}^{2} \cdot 3$ .

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Step 3.1

Reorder $3$ and ${(5 x + 1)}^{2}$ .

$\sqrt{{(5 x + 1)}^{2} \cdot 3}$

Step 3.2

Rewrite $1$ as $1^{2}$ .

$\sqrt{{(5 x + 1^{2})}^{2} \cdot 3}$

Step 4

Pull terms out from under the radical.

$(5 x + 1^{2}) \sqrt{3}$

Step 5

One to any power is one.

$(5 x + 1) \sqrt{3}$