Radical Expressions

Questions with Solutions for Grade 10

Grade 10 questions on how to use some important formuals to simplify radicals algebraic expressions with solutions are presented.

Important Formulas
A) If n and m are positive integers and ⁿ√y is a real number, then
equation 1

Examples
1) √5 is a real number and therefore

2) ³√(-7) is a real number and therefore
equation 3

B) If n is an EVEN positive integer then
equation 4

Examples

C) If n is an ODD positive integer then
equation 6

Examples

Questions With Answers

Rewrite, if possible, the following expressions without radicals (simplify)

equation 8

Solutions to the Above Problems

The index of the radical 3 is odd and equal to the power of the radicand.

since √x is a real number, x is positive and therefore |x| = x.

is not a real number since -x² - 1 is always negative.
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The index 8 is even and equal to the power of the radicand.
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The index 10 of the radical is even and equal to the power of the radicand.
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The index 3 of the radical is odd and equal to the power of the radicand.
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Even index and power of radicand.

Even index and power of radicand.