(m.) (4-2sqrt10)/(sqrt50)

Apply Quotient Rule: Apply the quotient rule of radicals to simplify sqrt(50). sqrt(50) = sqrt(25 × 2) = sqrt(25) × sqrt(2) = 5sqrt(2)Rewrite with Simplified Denominator: Rewrite the original expression with the simplified denominator. (4 - 2sqrt(10)) / (sqrt(50)) = (4 - 2sqrt(10)) / (5sqrt(2))Rationalize Denominator: Rationalize the denominator by multiplying the numerator and the denominator by sqrt(2). (4 - 2sqrt(10)) / (5sqrt(2)) × (sqrt(2) / sqrt(2)) = (4sqrt(2) - 2sqrt(10) × sqrt(2)) / (5sqrt(2) × sqrt(2))Simplify Numerator and Denominator: Simplify the numerator and the denominator. (4sqrt(2) - 2sqrt(20)) / (5 × 2) = (4sqrt(2) - 2sqrt(4 × 5)) / 10Simplify Square Root: Simplify the square root in the numerator. sqrt(20) = sqrt(4 × 5) = sqrt(4) × sqrt(5) = 2sqrt(5)Substitute Simplified Square Root: Substitute the simplified square root back into the numerator. (4sqrt(2) - 2 × 2sqrt(5)) / 10 = (4sqrt(2) - 4sqrt(5)) / 10Final Simplification: Simplify the expression by dividing both terms in the numerator by 10. (4sqrt(2) / 10) - (4sqrt(5) / 10) = (2/5)sqrt(2) - (2/5)sqrt(5)

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(m.) $\frac{4-2 \sqrt{10}}{\sqrt{50}}$

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Algebra 1

Simplify radical expressions involving fractions

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Q. (m.)

\frac{4-2 \sqrt{10}}{\sqrt{50}}

Apply Quotient Rule: Apply the quotient rule of radicals to simplify $\sqrt{50}$ . $\sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5\sqrt{2}$
Rewrite with Simplified Denominator: Rewrite the original expression with the simplified denominator. $\newline$ $(4 - 2\sqrt{10}) / (\sqrt{50}) = (4 - 2\sqrt{10}) / (5\sqrt{2})$
Rationalize Denominator: Rationalize the denominator by multiplying the numerator and the denominator by $\sqrt{2}$ . $\frac{4 - 2\sqrt{10}}{5\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{4\sqrt{2} - 2\sqrt{10} \times \sqrt{2}}{5\sqrt{2} \times \sqrt{2}}$
Simplify Numerator and Denominator: Simplify the numerator and the denominator. $(4\sqrt{2} - 2\sqrt{20}) / (5 \times 2) = (4\sqrt{2} - 2\sqrt{4 \times 5}) / 10$
Simplify Square Root: Simplify the square root in the numerator. $\sqrt{20} = \sqrt{4 \times 5} = \sqrt{4} \times \sqrt{5} = 2\sqrt{5}$
Substitute Simplified Square Root: Substitute the simplified square root back into the numerator. $\newline$ $(4\sqrt{2} - 2 \times 2\sqrt{5}) / 10 = (4\sqrt{2} - 4\sqrt{5}) / 10$
Final Simplification: Simplify the expression by dividing both terms in the numerator by $10$ . $\frac{4\sqrt{2}}{10}$ - $\frac{4\sqrt{5}}{10}$ = $\frac{2}{5}$ \sqrt{ $2$ } - $\frac{2}{5}$ \sqrt{ $5$ }