Simplify 3/14 square root of 98

$\frac{3}{14} \sqrt{98}$

Step 1

Rewrite $98$ as $7^{2} \cdot 2$ .

Factor $49$ out of $98$ .

$\frac{3}{14} \cdot \sqrt{49 (2)}$

Rewrite $49$ as $7^{2}$ .

$\frac{3}{14} \cdot \sqrt{7^{2} \cdot 2}$

$\frac{3}{14} \cdot \sqrt{7^{2} \cdot 2}$

Step 2

Pull terms out from under the radical.

$\frac{3}{14} \cdot (7 \sqrt{2})$

Step 3

Cancel the common factor of $7$ .

Factor $7$ out of $14$ .

$\frac{3}{7 (2)} \cdot (7 \sqrt{2})$

Factor $7$ out of $7 \sqrt{2}$ .

$\frac{3}{7 (2)} \cdot (7 (\sqrt{2}))$

Cancel the common factor.

$\frac{3}{7 \cdot 2} \cdot (7 \sqrt{2})$

Rewrite the expression.

$\frac{3}{2} \cdot \sqrt{2}$

$\frac{3}{2} \cdot \sqrt{2}$

Step 4

Combine $\frac{3}{2}$ and $\sqrt{2}$ .

$\frac{3 \sqrt{2}}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{3 \sqrt{2}}{2}$

Decimal Form:

$2.12132034 \dots$

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