square root of 175 in radical form
Understand the Problem
The question is asking for the square root of 175 expressed in radical form, which involves simplifying the square root by factoring out perfect squares.
Answer
$5\sqrt{7}$
Answer for screen readers
The square root of 175 expressed in radical form is $5\sqrt{7}$.
Steps to Solve
- Factor 175 into its prime factors
We start by factoring 175.
$$ 175 = 5 \times 35 $$
Next, we can factor 35:
$$ 35 = 5 \times 7 $$
So, we have:
$$ 175 = 5^2 \times 7 $$
- Apply the square root property
Now, we can apply the square root property. The square root of a product can be separated into the product of the square roots:
$$ \sqrt{175} = \sqrt{5^2 \times 7} $$
- Simplify the expression
We separate the square root:
$$ \sqrt{175} = \sqrt{5^2} \times \sqrt{7} $$
Calculating $\sqrt{5^2}$ gives us 5:
$$ \sqrt{175} = 5 \sqrt{7} $$
The square root of 175 expressed in radical form is $5\sqrt{7}$.
More Information
This simplification shows how to extract perfect squares from under a square root. The square root of 175 does not simplify to a whole number because 7 is not a perfect square, but it can be expressed neatly in radical form.
Tips
- A common mistake is to overlook the factorization process, leading to an incorrect square root. Always make sure to factor completely.
