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(2-3sqrt2)/(sqrt18)

$\frac{2-3 \sqrt{2}}{\sqrt{18}}$

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Simplify radical expressions involving fractions

Full solution

Q.

\frac{2-3 \sqrt{2}}{\sqrt{18}}

Apply Quotient Rule of Radical: Apply the quotient rule of radical to $\sqrt{18}$ . $\sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2}$
Find Square Root of $9$ : Find the square root of $9$ , which is a perfect square. $\sqrt{9} = 3$
Rewrite $\sqrt{18}$ : Now, rewrite $\sqrt{18}$ using the product found in the previous steps. $\newline$ $\sqrt{18} = \sqrt{9} \times \sqrt{2} = 3 \times \sqrt{2}$
Divide by Simplified Form: Divide the original expression by the simplified form of $\sqrt{18}$ . $\frac{2 - 3\sqrt{2}}{\sqrt{18}} = \frac{2 - 3\sqrt{2}}{3 \times \sqrt{2}}$
Simplify by Dividing: Simplify the expression by dividing both terms in the numerator by $3 \times \sqrt{2}$ . $\newline$ $\frac{2}{3 \times \sqrt{2}}$ - $\frac{3\sqrt{2}}{3 \times \sqrt{2}}$
Simplify Each Term: Simplify each term separately. $\newline$ First term: $\frac{2}{3 \times \sqrt{2}} = \frac{2}{3\sqrt{2}}$ $\newline$ Second term: $\frac{3\sqrt{2}}{3 \times \sqrt{2}} = 1$
Combine Simplified Terms: Combine the simplified terms. $\left(\frac{2}{3\sqrt{2}}\right) - 1$
Rationalize Denominator: Rationalize the denominator of the first term by multiplying the numerator and denominator by $\sqrt{2}$ . $\frac{2 \times \sqrt{2}}{3 \times \sqrt{2} \times \sqrt{2}} - 1$
Simplify Denominator: Simplify the denominator of the first term. $\newline$ $(2 \times \sqrt{2}) / (3 \times 2) - 1$
Perform Division: Perform the division in the first term. $\newline$ $(2 \times \sqrt{2}) / 6 - 1$
Simplify First Term: Simplify the first term by dividing $2$ by $6$ . $\left(\frac{\sqrt{2}}{3}\right) - 1$

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