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Simplify the following: 1. sqrt(12) 2. sqrt(18)/sqrt(1) 3. cubert(18) * 3sqrt(7) 4. sqrt(26/4)
Mathematics
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Step-by-step solution
12 stepsHere are the solutions to the simplification problems:
- Simplify .
Find the largest perfect square factor of 12.
$$ 12 = 4 \times 3 $$Apply the property .
$$ \sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} $$Simplify the perfect square root.
$$ \sqrt{4} = 2 $$ $$ 2 \times \sqrt{3} = 2\sqrt{3} $$ The simplified expression is $\boxed{2\sqrt{3}}$.2. Simplify .
Simplify the denominator.
$$ \sqrt{9} = 3 $$Rewrite the expression and simplify the numerator.
$$ \frac{\sqrt{18}}{3} = \frac{\sqrt{9 \times 2}}{3} = \frac{\sqrt{9} \times \sqrt{2}}{3} $$Simplify the perfect square root and cancel common factors.
$$ \frac{3\sqrt{2}}{3} = \sqrt{2} $$ The simplified expression is $\boxed{\sqrt{2}}$.3. Simplify .
Apply the property .
$$ \sqrt[3]{\frac{3}{7}} = \frac{\sqrt[3]{3}}{\sqrt[3]{7}} $$Rationalize the denominator by multiplying the numerator and denominator by .
$$ \frac{\sqrt[3]{3}}{\sqrt[3]{7}} \times \frac{\sqrt[3]{7^2}}{\sqrt[3]{7^2}} = \frac{\sqrt[3]{3 \times 49}}{\sqrt[3]{7^3}} $$Simplify the denominator.
$$ \frac{\sqrt[3]{147}}{7} $$ The simplified expression is $\boxed{\frac{\sqrt[3]{147}}{7}}$.4. Simplify .
Apply the property .
$$ \sqrt{\frac{26}{4}} = \frac{\sqrt{26}}{\sqrt{4}} $$Simplify the denominator.
$$ \sqrt{4} = 2 $$Rewrite the expression.
$$ \frac{\sqrt{26}}{2} $$ The simplified expression is $\boxed{\frac{\sqrt{26}}{2}}$.
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