Q&A for How to Divide Square Roots

√5 / 5 cannot be rationalized, simplified, or reduced. All you could do is to divide √5 (2.236) by 5.

You need to rationalize the denominator, since a denominator cannot have a square root. To do this, multiply the numerator and the denominator by sqrt*2: 1 x sqrt*2 = sqrt*2 sqrt*2 x sqrt*2 = 2. So it simplifies to sqrt*2/2.

Anything (other than zero) divided by itself is 1.

First find the square root of 35, then multiply by 6.

You can square the number you want to divide by and then put this new number directly under the 35 inside the square root. Generally, for dividing by x: (√35) / x = √35 / √(x^2 ) = √(35/x^2 ). As an example, if the number you want to divide by is 5, then: (√35) / 5 = √35 / √25 = √(35/25) = √(7/5) = √1.4.

You need to rationalize the denominator, since you can't have a square root in the denominator. To do this, multiply the numerator and denominator by sqrt*15: 9 x sqrt*15 = 9sqrt*15 sqrt*15 x sqrt*15 = 15. So this simplifies to 9sqrt*15/15.

sqrt*2 + 2/2 is already simplified, since there is a binomial in the numerator, and there is no factor common to each term in the numerator and denominator. To find the exact value, you will need to use a calculator.

No.

5√3 / 3√3: the two √3 's cancel each other. What's left is 5/3, or 1 2/3.

The rule is to remove radicals from denominators. In this case, do it by multiplying by the fraction (√5/√5) (which is the equivalent of multiplying by 1 and thus not changing the value of the original expression). So the solution looks like this: (7 / √5)(√5 / √5) = (7√5) / 5. That could be expressed as (7/5)(√5).

Take the expression 1 / √10. Rationalize the denominator by multiplying both numerator and denominator by √10: (1)(√10) / (√10)(√10) = √10 / 10. That's the answer.

√x / x² cannot be simplified, rationalized, or reduced. In other words, √x cannot be divided by x² to find a simpler result.

√10 / √15 = √(2x5) / (3x5) = (√2 x √5) / (√3 x √5). Canceling the two √5's leaves us with √2 / √3. Multiply both the numerator and the denominator by √3: √2 x √3 / √3 x √3 = √(2x3) / √(3x3) = √6 / 3.

The square root of 3 is roughly 1.7.

See Calculate a Square Root by Hand .

Divide the denominator into the decimal term, not the root term. For example, [(2.5)√3] / 5 = (0.5)√3.

It isn't. √420 = √[(4)(105)] = 2√105.

√2 / √3 cannot be reduced or simplified. All you can do is divide 1.414 by 1.732.

The simplest form is 5 + 2√6.

√99 / √9 = √[(9)(11)] / √9 = 3√11 / 3 = √11.

Yes. √6 / √3 = √(6/3) = √2.

One (√6) cancels the other. 4√6 / 5√6 = 4/5.

6 / √3 = (6 / √3)(√3 / √3) = 6√3 / √3√3 = 6√3 / 3 = 2√3. That's called "rationalizing the denominator," which means eliminating any roots from the denominator, which is a form of simplifying a fraction.

If you're using a calculator, then the easiest way is to find the square root of 1.67 (or 5/3). Another way is to evaluate √5 and √3 separately and then divide the first value by the second.

(√2) / 2 = 1.414 / 2 = 0.707.

Yes. For example, (3)(√2) = (3)(1.414) = 4.242.

Let's look at the numerator first: (√3)^5 = (√3)(√3)(√3)(√3)(√3) = (3)(3)(√3) = 9√3. Now the denominator: (√27)^-2 = 1/(√27)² = 1/(3√3)² = 1/[(9)(3)] = 1/27. Now do the division: (9√3) / (1/27) = (9√3)(27) = 243√3.

While that expression can be evaluated, it cannot be simplified.

In general, you remove a square root by multiplying by that same square root. (For example, √2 multiplied by √2 gives us 2.) You encounter this problem most often when there's a square root in the denominator of a fraction. Math purists don't like this, and so we "rationalize the denominator" by multiplying the fraction by another fraction equal to 1, consisting of the square root divided by itself. For example, we can rationalize the denominator of the fraction (5 / √3) by multiplying that fraction by (√3/√3). The result is (5√3 / 3). We still have a square root, but it's in the numerator instead of the denominator (which is considered an improvement).

30 / 18² = 30 / 324 = 0.0925. In case you meant 30 / √18, that's 30 / 3√2 = 10/√2 = 10√2 / 2 = 5√2.