Understanding Radicals

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Math › Understanding Radicals

Questions 1 - 10

Convert the radical to exponential notation.

$\small \sqrt[4]{13}$

$13^{\frac{1}{4}}$

$\small \sqrt{13^4}$

$\small 169$

$\small 13^4$

Explanation

Remember that any term outside the radical will be in the denominator of the exponent.

$\sqrt[b]{x^a}=x^{\frac{a}{b}}$

Since does not have any roots, we are simply raising it to the one-fourth power.

$\sqrt[4]{13}=13^{\frac{1}{4}}$

Convert the radical to exponential notation.

$\small \sqrt[4]{13}$

$13^{\frac{1}{4}}$

$\small \sqrt{13^4}$

$\small 169$

$\small 13^4$

Explanation

Remember that any term outside the radical will be in the denominator of the exponent.

$\sqrt[b]{x^a}=x^{\frac{a}{b}}$

Since does not have any roots, we are simply raising it to the one-fourth power.

$\sqrt[4]{13}=13^{\frac{1}{4}}$

Which fraction is equivalent to $\frac{x^{\frac{5}{2}}}{x^{\frac{1}{2}}+y^{\frac{1}{2}}}$ ?

$\frac{x^3-x^{\frac{5}{2}}y^\frac{1}{2}}{x-y}$

$\frac{x^3-x^{\frac{5}{2}}y^\frac{1}{2}}{x+y}$

$\frac{x^3+x^{\frac{5}{2}}y^\frac{1}{2}}{x-y}$

$\frac{x^3+x^{\frac{5}{2}}y^\frac{1}{2}}{x+y}$

Explanation

Multiply the numerator and denominator by the compliment of the denominator:

$=\frac{x^{\frac{5}{2}}}{x^{\frac{1}{2}}+y^{\frac{1}{2}}} \cdot \frac{x^{\frac{1}{2}}-y^{\frac{1}{2}}}{x^{\frac{1}{2}}-y^{\frac{1}{2}}}$

Simplify the expression:

$=\frac{x^3-x^{\frac{5}{2}}y^\frac{1}{2}}{x-y}$

Which fraction is equivalent to $\frac{x^{\frac{5}{2}}}{x^{\frac{1}{2}}+y^{\frac{1}{2}}}$ ?

$\frac{x^3-x^{\frac{5}{2}}y^\frac{1}{2}}{x-y}$

$\frac{x^3-x^{\frac{5}{2}}y^\frac{1}{2}}{x+y}$

$\frac{x^3+x^{\frac{5}{2}}y^\frac{1}{2}}{x-y}$

$\frac{x^3+x^{\frac{5}{2}}y^\frac{1}{2}}{x+y}$

Explanation

Multiply the numerator and denominator by the compliment of the denominator:

$=\frac{x^{\frac{5}{2}}}{x^{\frac{1}{2}}+y^{\frac{1}{2}}} \cdot \frac{x^{\frac{1}{2}}-y^{\frac{1}{2}}}{x^{\frac{1}{2}}-y^{\frac{1}{2}}}$

Simplify the expression:

$=\frac{x^3-x^{\frac{5}{2}}y^\frac{1}{2}}{x-y}$

Choose the fraction equivalent to $\frac{x^{\frac{1}{2}}-y^{\frac{1}{2}}}{x^{\frac{1}{2}}+y^{\frac{1}{2}}}$ .

$\frac{x-2x^{\frac{1}{2}}y^{\frac{1}{2}}+y}{x-y}$

$\frac{x+2x^{\frac{1}{2}}y^{\frac{1}{2}}+y}{x-y}$

$\frac{x+2x^{\frac{1}{2}}y^{\frac{1}{2}}+y}{x+y}$

$\frac{x-2x^{\frac{1}{2}}y^{\frac{1}{2}}+y}{x+y}$

Explanation

Multiply the numerator and denominator by the compliment of the denominator:

$=\frac{x^{\frac{1}{2}}-y^{\frac{1}{2}}}{x^{\frac{1}{2}}+y^{\frac{1}{2}}}$ $\cdot \frac{x^{\frac{1}{2}}-y^{\frac{1}{2}}}{x^{\frac{1}{2}}-y^{\frac{1}{2}}}$

Simplify the expression:

$=\frac{x-2x^{\frac{1}{2}}y^{\frac{1}{2}}+y}{x-y}$

Choose the fraction equivalent to $\frac{x^{\frac{1}{2}}-y^{\frac{1}{2}}}{x^{\frac{1}{2}}+y^{\frac{1}{2}}}$ .

$\frac{x-2x^{\frac{1}{2}}y^{\frac{1}{2}}+y}{x-y}$

$\frac{x+2x^{\frac{1}{2}}y^{\frac{1}{2}}+y}{x-y}$

$\frac{x+2x^{\frac{1}{2}}y^{\frac{1}{2}}+y}{x+y}$

$\frac{x-2x^{\frac{1}{2}}y^{\frac{1}{2}}+y}{x+y}$

Explanation

Multiply the numerator and denominator by the compliment of the denominator:

$=\frac{x^{\frac{1}{2}}-y^{\frac{1}{2}}}{x^{\frac{1}{2}}+y^{\frac{1}{2}}}$ $\cdot \frac{x^{\frac{1}{2}}-y^{\frac{1}{2}}}{x^{\frac{1}{2}}-y^{\frac{1}{2}}}$

Simplify the expression:

$=\frac{x-2x^{\frac{1}{2}}y^{\frac{1}{2}}+y}{x-y}$

Simplify: $(\frac{2^4a}{a^2b^{-1}})^{\frac{-1}{2}}$