Please help me!!! Any math people out there?

Question

I am usually pretty good at math, but I am struggling. I have been out of school for 3 years now starting college this year. I'm not asking for answers--I need someone to please show me step by step how to simplify a radical...example Square root of 25. Square root of 45. How do I do it????? Please help

Answer 1

SQRT (25) = 5 .............. since 5^2 = 25

SQRT (45) = SQRT (9 * 5) = SQRT (9) * SQRT (5)
= 3 * SQRT (5) ............... since 3^2 = 9

Look for a factor of the number under the SQRT which is a perfect square (such as 9 in the example above).

Answer 2

No problem. Simplifying a radical is simple once you get the hang of it. The main idea is that the number under the radical is composed of several factors. The first step is list a set of obvious factors for your number. For example, 45=9 x 5. 5 is prime so that number can't change. On the other hand, 9 = 3 x 3. So for right now you have square root of 45= square root of 3 x 3 x 5. This next step is very important. every time a number appears twice, circle the pair. The pair will come outside the radical as that number to the first power. Basically, since 3 appears twice in the list of factors, it will leave the inside an come out as 3 NOT 9! numbers that appear only once will stay in the radical. So since 5 appears once, it will stay inside the radical. if you have different numbers , pairs of different numbers, multiple them after they leave the radical. Same rule applies to inside the radical. So for our final answer square root of 45= 3square root 5.
another example is square root of 129. Its factors are 3 x 43. since both are prime the simplified form is square root of 129.
another is square root of 360. 2 x 180 = 2 x 90 x 2 = 2 x 2 x 2 x 45 = 2x2x2x5x9= 2 x 2 x 2 x 5 x 3 x 3. since their are (3) 2's 2 of the 2's come outside the radical as 2 and the other 2 stays inside. the (2) 3's come out as 3. 5 stays in since their is only one 5. so now we have (2 x 3) square root (5 x 2)= 6 square root of 10. finally, an easy way to check your answer is to square the number outside of the radical and then multiply it by the number in the radical. For example, since square root of 360 was the staring number, take 6 and square it, = 36. then multiply by 10, = 360 therefore the answer is right. After this is mastered you can move onto rationalizing the denominator etc. here is a site if you ever need more help. http://www.algebralab.org/lessons/lesson.aspx?file=algebra_radical_simplify.xml
http://www.purplemath.com/modules/radicals.htm
http://www.purplemath.com/modules/radicals4.htm
good luck.
p.s. please pick me as best answer.

Answer 3

Simplifying a radical means taking out as much as possible.

For perfect squares (numbers which have whole number square roots) this is very easy:

25 is the product of 5 * 5. So to simplify the s1. root of 25, the answer is simply 5.

A number like 45 is not a perfect square, it does not have a whole number square root. But it can be simplified into numbers that are perfect squares. 45 = 5 * 9...9 is a perfect square.

So the answer is this:

SR 45 = SR (9*5) = SR (9) * SR (5) = 3 * SR (5)

Answer 4

It is good to know some squares like for:

1 is 1
4 is 2
9 is 3
16 is 4
25 is 5
36 is 6
49 is 7
64 is 8
81 is 9
100 is 10
anything other than the nice ones can be found using a calculator if you need an exact answer. Most of the time math teachers don't mind if you leave it in radical form like sqrt(48) or sqrt(77) , one last thing is you can partially find the square root of a number like sqrt(12) is sqrt (3*4) which can be written as 2*sqrt(3) by finding the root of what you know and leaving what you don't know under the radical sign.
for exams that offer multiple choice answers use approximation.
sqrt(35) = just under 6 so 5.8 to 5.9 since we know the root of 36 to be 6. And we know the answer to be grater than 5 since the given number is greater than 25.

Answer 5

sqrt(25) = 5. 5 x 5 = 25 (or use the calc)

sqrt(45) = sqrt( 9 x 5) = sqrt(9) x sqrt(5) = 3 sqrt(5)

You can only add or sub coeff with same radicals like you do with same orders variables so

sqrt(45) + sqrt(125) = 3 sqrt(5) + 5 sqrt(5) = 8 sqrt(5)

Hope it helps

Answer 6

determining the squareroots of numbers isn't usually taught in college. you'll be using calculators for that purpose.