Search for:. Simplifying Square Roots Using the Product Rule to Simplify Square Roots To simplify a square root, we rewrite it such that there are no perfect squares in the radicand. How To: Given a square root radical expression, use the product rule to simplify it. Factor any perfect squares from the radicand. Write the radical expression as a product of radical expressions. Example 4. We have to factor 42 and see if it has any square factors.
We can begin the factoring in any way. We now see that 42 has no square factors -- because no factor is repeated. Compare Example 1 and Problem 2 of the previous Lesson. Example 5. We must look for square factors, which will be factors that are repeated. Problem 1.
To simplify a radical, why do we look for square factors? To see the answer, pass your mouse over the colored area. To cover the answer again, click "Refresh" "Reload". Do the problem yourself first! In order to take its square root out of the radical. Happy New Year and Information 2. Real life Math 3. Math tip - Radicals 4. New in IntMath - Integrator, from Mathematica 5.
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Go to: Online algebra solver. The rules for exponents and roots still apply to these variables. Give positive solutions to even roots. That means that 4 or any positive number actually has two square roots: one positive number and one negative. The odd root of a negative number is always negative, and the odd root of a positive number is always positive. Use the absolute value symbol to make a variable positive. Variables are tricky: we don't know whether they represent a positive or a negative number.
Since the square root or any even root function must always give a positive answer, we make sure this happens by using the absolute value symbol around the answers, like this: x. This symbol just means "make this value positive. To make sure the solution to the root is positive, add absolute value symbols around that term: x.
You can only take something out from under a radical if it's a factor. Not Helpful 2 Helpful 4. A rectangle has sides of 4 and 6 units. On each of its four sides, square are drawn externally. Their centers form another quadrilateral. What is the area in sq.
You'll have to draw a diagram of this. You'll see that triangles can be drawn external to all four sides of the new quadrilateral. By the Pythagorean theorem you can find the sides of the quadrilateral, all of which turn out to be 5 units, so that the quadrilateral's area is 25 square units.
Not Helpful 1 Helpful 2. How do you match a radical expression with the equivalent exponential expression? You can rewrite any radical expression as a fractional exponent. If there is an exponent already inside the square root, it becomes the top number of the new exponent.
Not Helpful 0 Helpful 0. Include your email address to get a message when this question is answered. By using this service, some information may be shared with YouTube. You can find online tools or apps that will simplify a radical expression for you. You can use these to check your work. Helpful 0 Not Helpful 0. For complicated problems, you might need to use more than one of these methods. For instance, you might first multiply a square root with a cube root, then simplify further, then simplify a fraction.
Submit a Tip All tip submissions are carefully reviewed before being published. The square root or any even root of a negative number can't be simplified without using complex numbers. Related wikiHows How to.
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