SOLUTION: Simplify. Assume x represents a positive number. The square root of 175x to the fourth power. Please help me with this. I don't even know where to begin.

Question 87472: Simplify. Assume x represents a positive number.
The square root of 175x to the fourth power.
Please help me with this. I don't even know where to begin.
Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!

You should begin with my Lesson Plans in algebra.com dealing with square roots, or see my own website by clicking on my tutor name "rapaljer" anywhere in algebra.com. Then there are TWO different pages that will be helpful to you. The first page is called "MATH IN LIVING COLOR", go to "Basic Algebra", and then look in "Chapter 5" in the first section in Chapter 5. For complete explanations, go back to my homepage, then click on "Basic Algebra", look for "Samples from Basic Algebra: One Step at a Time", look for Chapter 5, then look in the first section. My website, like algebra.com, is ALL FREE!!

Now, to solve your problem. First you must separate the given square root into two square roots, and sort out all the "perfect square factors", placing these in the first square root. Find a perfect square that divides into 175. Hint: try 25, which divides into 175, 7 times. Also, notice that x^4 is a perfect square. So put the 25x^4 in the first square root. The "left-over" factor is 7, so put that in the second square root:

Now, do the square root of the perfect square, which everyone can do! For the second square root, you can't do it, so leave it alone:

That should do it!!

R^2 Retired from SCC

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