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This algebra 1 math tutorial from NutshellMath offers targeted homework help with simplifying radicals and radical expressions. The instruction is focused on homework problems 6-20 on page 433 of the Algebra: Tools for a Changing World text from Prentice Hall.
Radicals and radical expressions are algebraic terms or expressions that involve square roots. A radical or radical expression is considered simplified completely when there are no perfect square factors or fractions under the radical, and no radical terms are in the denominator of a fraction.
This tutorial focuses upon simplification of radical terms. The two major properties of radicals introduced are for multiplication and division of radicals. These properties state that a square root of a product is equal to the product of the square roots of the factors, and that the square root of a quotient is equal to the quotient of the square roots of the dividend and divisor. Using these properties, it is possible to completely simplify any radical or radical expression.
The major method of simplifying radicals is to successively factor a whole number under a radical in order to remove perfect squares. Factoring a number under a radical into a product of a perfect square and another number permits the perfect square to be square rooted and removed from the radical, using the multiplicative property of radicals.
To remove radicals from denominators, it is possible to multiply a radical term by an identity of the radical in the denominator over itself. Doing so will square the radical in the denominator, removing the radical sign, and place the same radical term in the numerator. This is best demonstrated by the fact that 1 divided by the square root of x is equal to the square root of x, divided by x.
To remove fractions from under radicals, it is necessary to separate the denominator into a separate radical and remove it as any other radical in a denominator.
Using the tips presented in this tutorial, it is possible to effectively simplify radicals, and solve homework problems involving simplification of radical terms and expressions.
This algebra 1 math tutorial from NutshellMath offers targeted homework help with simplifying radicals and radical expressions. The instruction is focused on homework problems 6-20 on page 433 of the Algebra: Tools for a Changing World text from Prentice Hall.
Radicals and radical expressions are algebraic terms or expressions that involve square roots. A radical or radical expression is considered simplified completely when there are no perfect square factors or fractions under the radical, and no radical terms are in the denominator of a fraction.
This tutorial focuses upon simplification of radical terms. The two major properties of radicals introduced are for multiplication and division of radicals. These properties state that a square root of a product is equal to the product of the square roots of the factors, and that the square root of a quotient is equal to the quotient of the square roots of the dividend and divisor. Using these properties, it is possible to completely simplify any radical or radical expression.
The major method of simplifying radicals is to successively factor a whole number under a radical in order to remove perfect squares. Factoring a number under a radical into a product of a perfect square and another number permits the perfect square to be square rooted and removed from the radical, using the multiplicative property of radicals.
To remove radicals from denominators, it is possible to multiply a radical term by an identity of the radical in the denominator over itself. Doing so will square the radical in the denominator, removing the radical sign, and place the same radical term in the numerator. This is best demonstrated by the fact that 1 divided by the square root of x is equal to the square root of x, divided by x.
To remove fractions from under radicals, it is necessary to separate the denominator into a separate radical and remove it as any other radical in a denominator.
Using the tips presented in this tutorial, it is possible to effectively simplify radicals, and solve homework problems involving simplification of radical terms and expressions.