# How do you simplify #sqrt42 * sqrt12#?

All integers can be expressed as the product of prime numbers. In problems involving finding roots of integers it is often useful to start by expressing the integers as products of prime numbers.

From this example:

From the above factorisation:

By signing up, you agree to our Terms of Service and Privacy Policy

To simplify ( \sqrt{42} \times \sqrt{12} ), you multiply the numbers inside the square roots together:

[ \sqrt{42} \times \sqrt{12} = \sqrt{42 \times 12} ]

Then, you simplify the expression inside the square root:

[ 42 \times 12 = 504 ]

So,

[ \sqrt{42} \times \sqrt{12} = \sqrt{504} ]

Next, you find the largest perfect square that divides evenly into 504, which is 36:

[ 504 = 36 \times 14 ]

Therefore,

[ \sqrt{504} = \sqrt{36 \times 14} ]

[ = \sqrt{36} \times \sqrt{14} ]

[ = 6 \times \sqrt{14} ]

So,

[ \sqrt{42} \times \sqrt{12} = 6 \sqrt{14} ]

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7