Pre-Algebra Examples

$\sqrt{21} \sqrt{5} \sqrt{3} - \sqrt{140 a^{2}}$

Step 1

Combine using the product rule for radicals.

$\sqrt{21 \cdot 5} \sqrt{3} - \sqrt{140 a^{2}}$

Step 2

Combine using the product rule for radicals.

$\sqrt{21 \cdot 5 \cdot 3} - \sqrt{140 a^{2}}$

Step 3

Multiply $21$ by $5$ .

$\sqrt{105 \cdot 3} - \sqrt{140 a^{2}}$

Step 4

Multiply $105$ by $3$ .

$\sqrt{315} - \sqrt{140 a^{2}}$

Step 5

Rewrite $315$ as $3^{2} \cdot 35$ .

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Step 5.1

Factor $9$ out of $315$ .

$\sqrt{9 (35)} - \sqrt{140 a^{2}}$

Step 5.2

Rewrite $9$ as $3^{2}$ .

$\sqrt{3^{2} \cdot 35} - \sqrt{140 a^{2}}$

$\sqrt{3^{2} \cdot 35} - \sqrt{140 a^{2}}$

Step 6

Pull terms out from under the radical.

$3 \sqrt{35} - \sqrt{140 a^{2}}$

Step 7

Rewrite $140 a^{2}$ as ${(2 a)}^{2} \cdot 35$ .

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Step 7.1

Factor $4$ out of $140$ .

$3 \sqrt{35} - \sqrt{4 (35) a^{2}}$

Step 7.2

Rewrite $4$ as $2^{2}$ .

$3 \sqrt{35} - \sqrt{2^{2} \cdot 35 a^{2}}$

Step 7.3

Move $35$ .

$3 \sqrt{35} - \sqrt{2^{2} a^{2} \cdot 35}$

Step 7.4

Rewrite $2^{2} a^{2}$ as ${(2 a)}^{2}$ .

$3 \sqrt{35} - \sqrt{{(2 a)}^{2} \cdot 35}$

$3 \sqrt{35} - \sqrt{{(2 a)}^{2} \cdot 35}$

Step 8

Pull terms out from under the radical.

$3 \sqrt{35} - (2 a \sqrt{35})$

Step 9

Multiply $2$ by $- 1$ .

$3 \sqrt{35} - 2 a \sqrt{35}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$