Question

I don’t know how to do that it doesn’t make sense to me? Am i dividing it

Answer 1

`\sqrt[]{2025}\text{ = 45}`Step-by-step explanation:
`\begin{gathered} \text{Given:} \\ \sqrt[]{2025} \end{gathered}`

To find the square root of the number above, first let's break the number down into smaller factors to determine if it is a perfect square

`\begin{gathered} \text{First divide by 5 as it is divisible by it (last digit is 5)} \\ (2025)/(5)\text{ = }405 \\ 2025\text{ = 5 }*\text{ 405} \\ (405)/(5)\text{ = 81 (divisible by 5 as last digit is 5)} \\ 405\text{ = 5 }*81 \\ 2025\text{ = 5 }*5\text{ }*\text{ 81} \end{gathered}`

`\begin{gathered} We\text{ can break down 81 if we don't know its roots}\colon \\ 81\text{ divisible by 3 = }(81)/(3)\text{ = 27} \\ 27\text{ divided by 3 = }(27)/(3)\text{ = 9} \\ 9\text{ divided by 3 = }(9)/(3)\text{ = 3} \\ 3\text{ divided by 3 = 3/3 = 1} \\ \\ We\text{ divided 3 four times} \\ 81\text{ = 3}*3*3*3 \end{gathered}`

`\begin{gathered} \sqrt[]{2025}\text{ = }\sqrt[]{\text{(5}*5)*(3*3)*(3*3)} \\ we\text{ will take only one of the numbers appearing twice:} \\ =\text{ 5 }*\text{ 3 }*\text{ 3} \\ =\text{ 45} \\ \\ \text{Hence, we can say 45 }*\text{ 45 = 2025} \\ \text{and }\sqrt[]{2025}\text{ = 45} \end{gathered}`