Q&A for How to Simplify Radical Expressions

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How do I simplify radicals?

Community Answer

You can only take something out from under a radical if it's a factor. For instance, sqrt(64*(x+3)) can become 8*sqrt(x+3), but sqrt(64x + 3) cannot be simplified.

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Question

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. units) of this quadrilateral?

Donagan

Top Answerer

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.

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How do you match a radical expression with the equivalent exponential expression?

Myles_Schaller

Community Answer

You can rewrite any radical expression as a fractional exponent. For example, the square root of 5 is the same as 5 to the power of 1/2. The type of root determines the bottom number of the fraction, so the fourth root of 5 is the same as 5 to the power of 1/4. If there is an exponent already inside the square root, it becomes the top number of the new exponent. So the square root of (3^5) becomes 3 raised to the power of (5/2).

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How do I know if a radical expression is completely simplified?

I_l1ke_gam3s

Community Answer

If it cannot be broken down any further, you know that the radical expression is in simplest form.

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What is the simplest form of 5/(square root of a) + (square root of b)?

I_l1ke_gam3s

Community Answer

This is the simplest form and cannot be simplified any further so this is your answer in simplest form.

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