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Dividing Radicals
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Dividing Radicals – the Basics
Like with multiplying radicals, to divide radicals they must have the same INDEX. Remember, division is often written as a fraction. As with multiplying radicals, you can divide/reduce the coefficients to get the coefficient of the quotient, then divide/reduce the radicand to get the radicand of the quotient. The final basic fact you need to know is: to take the root of a fraction, you take the root of both the numerator and denominator. Lets try some examples…
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Are the indices the same? YEP!!! Let’s do this!
Divide num. & denom. by 2 Divide num. & denom. by 3 Divide num. & denom. by 25 Are the indices the same? YEP!!! Let’s do this! Divide/reduce the coefficients and radicands. Simplify your radical Are the indices the same? YEP!!! Let’s do this! Divide/reduce the coefficients and radicands. Simplify your radical. What happened to the denominator? Final check: are your radical and fraction completely simplified?
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How do I take the square root of a fraction?
Take the square root of the numerator and denominator separately. But make your life easier – simplify your fraction first. Now split it up and simplify. Divide num. & denom. by 7
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One of those really important math rules….
You know you need to simplify fractions completely, combine like terms, simplify radicand, etc. before you can say you have ‘finished’ a problem. One other rule you need to know is that you NEVER leave a radical in the denominator of a fraction! We will use our knowledge of simplifying radicals and of equivalent fractions to make sure we don’t break this rule!
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Rationalizing Denominators
Final check: are your radical and fraction completely simplified? Step 1 – simplify our fraction Step 2 – simplify our radicands Step 3 – rationalize the denominator Why do we still have a radical in the denominator? What would we need for the radical to simplify?
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