To simplify a square root: make the number inside the square root as small as possible (but still awhole number): Example: √12 is simpler as 2√3 Get your calculator and check if you want: they are both the same value! Here is the rule: whena and b arenot negative ...
For any number {eq}x \geq 0 {/eq}, the square root of {eq}x {/eq} is a nonnegative number {eq}\sqrt{x} {/eq} such that: {eq}\sqrt{x}^2 = x {/eq} It follows immediately that {eq}\sqrt{x^2} = x {/eq} An important vocabulary note: roots are often called radicals....
A General Note: The Product Rule for Simplifying Square Roots Ifaaandbbare nonnegative, the square root of the productababis equal to the product of the square roots ofaaandbb. √ab=√a⋅√bab=a⋅b How To: Given a square root radical expression, use the product rule to simplify it...
Simplify Notice that 9*5 = 45 Is there a perfect square that is a factor of 45? If so break down the expression, if not it is already simplified. Notice that 9*5 = 45 Use your calculator to check Simplify Simplify Simplifying may take more than one steps And can be worked different ...
A square root is a number that, when multiplied by itself, equals a specific number. For example, 6 is the square root of 36 because {eq}6\times 6=36 {/eq}. A square root will be both the positive and corresponding negative number. With 16, both 4 and -4 are the square roots:...
simplifyingradicals简化squareradicandroot Simplifying Radicals A square root of a number n is a number m such that m 2 = n. Every positive number has two square roots, one positive and one negative. Negative numbers have no real square roots. The square root of zero is zero. Simplifying Ra...
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Nominclature Rules Positive numbers Negative numbers Odd index number means Roots are always positive Even index numbers means Roots are both positive and negative Example: since both 4 and -4 squared will result in 16 Negative numbers Even index number, no real root Odd index number, always ...
Convertingrootsintofractionalexponents:AnyradicalexpressionForexamplemaybetransformedintoanexpressionwith=afractionalexponent.Thekeyistoremember5thatthefractional3exponentmustbeintheform (16)(−2)=(−2)1 16 2 5 3 powerroot NegativeExponents:Rememberthatanegativeintheexponentdoesnotmakethenumbernegative!Ifa...