Q&A for How to Multiply Square Roots

When you multiply a whole number by a square root, you just put the two together, with the whole number in front of the square root. For example, 2 * (square root of 3) = 2(square root of 3). If the square root has a whole number in front of it, multiply the whole numbers together. So 2 * 4(square root of 3) = 8(square root of 3).

√3 times √3 equals 3. Two times that is 6.

(4√5)/5. Since radicals are not supposed to be in the denominator, you multiply by √5/√5 to get (4√5)/5.

Generally we write 5√2 or calculate the square root of 2, which is 1.414, and then multiply it by 5. The answer would be 7.07.

The square root and the square cancel each other out, so the final answer is 5+7, which is 12.

It would be 2 x 2sqrt2 = 4sqrt2, this is the simplest form and cant be reduced any further.

It's an irrational number, which you could round to 2.45. Usually you would just use a calculator to find such a square root.

When multiplying an integer by a square root, you simply place the integer in front of the radical sign. So -1 x √3 is expressed as -1√3. You can use a calculator to find the exact product.

-6.

You simply place the whole number in front of the radical sign. For example, 2 x √2 would simply be expressed as 2√2. You can use a calculator to find the exact product.

The answer is 2√3. First, it would be written as √(2√12). Then, after simplification it would become √(2√3×4)=√(4√3), √4=2, 2√3.

The square root of the square root of a number is equal to the fourth root of that number.

Yes. (2)(16√6) = 32√6.

20 root 6. There is an imaginary one in front of the root symbol, so root 2 = 1 root 2. First multiply the numbers outside the root symbol. 20 times 1 is 20. Then you multiply the numbers inside the root symbol. 2 times 3 is 6. You can't simplify root 6, so your answer is 20 root 6.

Leave the number outside the square root alone, and multiply the root number.

The answer is 10. Since you have sqrt 2 multiplying by sqrt 2, that turns into sqrt 4, which is simplified as 2. So that would be 5 * 2, which is equal to 10.

(√3)(3 - √3) = 3√3 -(√3)(√3) = 3√3 - 3.

You leave the number outside of the square root alone, and you multiply the square roots. Then, you simplify your square root to the lowest it can be, and if it gives an integer, multiply the two. If it gives a square root again, just put the number that was originally outside next to your new square root.

(2 - √2)(2 + √2) = 4 +2√2 - 2√2 - 2 = 4 - 2 = 2.

5 sqrt 3 x sqrt 27 = 5 sqrt 3 x sqrt (9 x 3) = 5 sqrt 3 x 3 sqrt 3 = 15 sqrt (3 x 3) = 15 x 3= 45.

The easiest part of this would be squaring (the inverse of the square root) the 6 (6x6=36) before checking that the solution is a multiple of 3 (3x12=36) - they both indicate the answer is 36.

If you multiply √7 by √7, the product is 7.

(√3)(√2) = √[(3)(2)] = √6.

See Calculate a Square Root by Hand or use a calculator to find the result. Its exact value is 12.21.

(-4)²(-9)² = (16)(81) = 1296. (The square of a negative number is a positive number.)

(√3)(2√2) = 2√[(3)(2)] = 2√6. Leave it like that or further evaluate it: 2√6 = (2)(2.45) = 4.9.

√36 = 6. √(√36) = √6 = 2.45.

(√2)(√3) = √[(2)(3)] = √6.

(√2 - 2)² = (√2 - 2)(√2 - 2) = (√2)(√2) - 2√2 - 2√2 + 4 = (2) - 4√2 + 4 = 6 - 4√2. You can leave the answer in that form, or you could evaluate √2 as 1.414. Then 6 - 4√2 = 6 - 4(1.414) = 6 - (5.656) = 0.344. You could also evaluate √2 at the beginning and then evaluate (√2 - 2)², which would yield the same answer.

9√3 = (9)(1.732) = 15.59.