which expression is equivalent to the following expression: 3√40

Answer 1

To simplify the expression \( 3\sqrt{40} \), we can start by breaking down \( \sqrt{40} \).

We can factor \( 40 \) into its prime factors: \[ 40 = 4 \times 10 = 4 \times 2 \times 5 \]

Knowing that \( 4 \) is a perfect square, we can simplify \( \sqrt{40} \): \[ \sqrt{40} = \sqrt{4 \times 10} = \sqrt{4} \times \sqrt{10} = 2\sqrt{10} \]

Now, we can substitute this back into the original expression: \[ 3\sqrt{40} = 3(2\sqrt{10}) = 6\sqrt{10} \]

Therefore, the expression equivalent to \( 3\sqrt{40} \) is: \[ \boxed{6\sqrt{10}} \]

Answer 2

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Answer 3

To simplify the expression three square root of forty, we start by breaking down the square root of forty.

Forty can be factored into four times ten. Since four is a perfect square, we can simplify the square root of forty as follows:

The square root of forty equals the square root of four times the square root of ten. The square root of four is two.

So, we find that the square root of forty equals two times the square root of ten.

Now we substitute this back into the original expression:

Three square root of forty equals three times two square root of ten, which simplifies to six square root of ten.

Therefore, the expression equivalent to three square root of forty is six square root of ten.