Q&A for How to Simplify a Square Root

If something is written in its simplest radical form, that means that you have already found all possible roots and eliminated any radicals from the denominator of a fraction. A square root can’t be simplified any further if there are no 2 identical factors remaining and every term under the radical symbol is a prime number.

Start by multiplying the numerator and denominator by a radical that will eliminate the radical in the denominator. For example, if your fraction is 2/√7, multiply by √7/√7 to get 2√7/√49. This will simplify to 2√7/7. If possible, simplify the fraction by dividing out any common factors in the numerator and denominator.

Use the same procedure you would for simplifying square roots with numerical radicands. Bring any identical pairs of factors out of the radical to become the coefficient. For example, if you need to simplify √25a^3, change it to √5×5×a×a×a. Factor out 5 and a^2 to get 5a^2√a.

√18 = √(2x3x3) = 3√2. √8 = √(2x2x2) = 2√2. Then (3√2) - (2√2) = 1√2 = √2.

The square root of 841 is 29.

You have to factor 2sqrt8 further. To simplify the numbers you listed, the numbers in the root have to be equivalent so you can perform addition/subtraction. Try this: sqrt8 is 2 root 2. 2*2=4 plus the root. Your equation now is 4sqrt2- 4sqrt 2 + 3sqrt 2. 4sqrt2-4sqrt2=0. Your answer is 3sqrt 2.

25 is a whole number square root. X*X=25 What is X? 5*5=25. That means the square root of 25 is 5.

A "perfect" square is the square of a whole number, but 48 is the square of 6.928.

You have to make a factor tree. Move from top to bottom like this: 20 2-10 *-5-2 * means no further splits. what number(s) are repeated? 2 is repeated twice, 5 is only written once. Since 2 is repeated twice, the answer is 2sqrt5. However, if you have an odd number of repeats of one number, go up the tree once. EX: 40 2-20 *-2-10 *-*-2-5 2 repeated 3 times, 5 repeated once. That means your answer is 2sqrt10

√(16n²) = √[(4²)(n²)] = (4)(n) = 4n.

To divide easily with 2's is you add the numbers together like 5 times 2 = 10 and threes is basely the same but you add another number like 5 times 3 +5 +15 -- easy!

Since prime numbers are only divisible by themselves and one, a prime number's square root will not be an integer. Just type it into your calculator.

Use the order of operations, or PEMDAS. Parenthesis, Exponents Multiplication/Division, Addition/Subtraction . Your equation is 3+7 under a radical (square root symbol). 3+7=10. X*X=10 what is x? The problem is 10 has no root. You have to make a factor tree that has repeat numbers. EX: 10 could be 5 and 2. 5 cannot be divided again, nor 2. If you make a tree out of 16 you have 2 and 8. 8 can be divided again. 2-4-2. 2-2-2-2 So 16's square root would be 4.

8 + 215 = 223. 10 - 221 = -211. Subtracting a negative 211 is the same as adding a positive 211. So the answer is 223 + 211 = 434.

√2 does not simplify as described above. The simplest "form" of √2 is 1.414.

I am assuming you mean this equation: (4*the square root of 12)/2. First, you divide the top and bottom of the equation/division line by 2. The bottom cancels out into a 1, so now it is just 4*the square root of 12. Now you have to simplify the 12 inside the radical (square root symbol). Find the largest perfect square number the radicand (12) is divisible by and divide 12 by that number. Then multiply its square root to the outside 4. The perfect square number is 4, and the square root is 2. The fully simplified version would be 2*the square root of 3.

Use a calculator, or see the wikiHow article Calculate a Square Root by Hand .

That's 10 x 1.414.

√½ = √1 / √2 = 1 / √2. Then rationalize the denominator: (1)(√2) / √2)(√2) = √2 / 2. You can verify this answer by squaring (√2 / 2): (√2 / 2)(√2 / 2) = 2/4 = ½.

1 / √5 = (1)(√5) / (√5)(√5) = √5 / 5.

(√5 + √2)(√5 + √2) = 5 + √5√2 + √5√2 + 2 = 7 + √10 + √10 = 7 + 2√10.

7√25 = 7√5² = 7 x 5 = 35.

Multiply both numerator and denominator by the square root in the denominator. This simplifies the denominator by eliminating its radical sign, which is what you want to do. You may, however, wind up with a radical sign in the numerator, which is okay. For example, let's say you want to simplify the fraction 4/√5. Multiply both numerator and denominator by √5: (4)(√5) / (√5)(√5) = (4√5) / 5. That's as simplified as that fraction can get, unless you want to substitute 2.236 for √5, then multiply by 4 and divide by 5 to fully evaluate the fraction.

-√12 = -√(4 x 3) = -2√3.

141.4213. One way to view this is to express 20,000 as 2 x 10^4, so that the square root is √2 x 10² = 1.414213 x 100.

5 / (2√3) = (5)(√3) / (2√3)(√3) = (5√3) / (2 x 3) = (5√3) / 6.

√77 does not simplify. You just have to use a calculator or a square-root table or calculate it "by hand."

√32 = √(2 x 16) = √(2 x 4²) = 4√2.

5√50 + 6√32 = 5√(2 x 25) + 6√(2 x 16) = 5√(2 x 5²) + 6√(2 x 4²) = (5 x 5)√2 + (6 x 4)√2 = 25√2 + 24√2 = 49√2.

(-5)(-5) = +25.