Question
Let's find the square root of the fo \( \begin{array}{lll}\text { (a) } 5^{2} \times 8^{2} & \text { (b) } 4225 & \text { (c) } 10609\end{array} \)
Ask by Lynch Valdez. in India
Feb 20,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The square roots are:
- (a) 40
- (b) 65
- (c) 103
Solution
Calculate the value by following steps:
- step0: Calculate:
\(\sqrt{10609}\)
- step1: Write in exponential form:
\(\sqrt{103^{2}}\)
- step2: Simplify the root:
\(103\)
Calculate or simplify the expression \( \sqrt(4225) \).
Calculate the value by following steps:
- step0: Calculate:
\(\sqrt{4225}\)
- step1: Write in exponential form:
\(\sqrt{65^{2}}\)
- step2: Simplify the root:
\(65\)
Calculate or simplify the expression \( \sqrt(5^2 * 8^2) \).
Calculate the value by following steps:
- step0: Calculate:
\(\sqrt{5^{2}\times 8^{2}}\)
- step1: Multiply the numbers:
\(\sqrt{40^{2}}\)
- step2: Simplify the root:
\(40\)
Here are the square roots for each of the given expressions:
(a) For \( \sqrt{5^{2} \times 8^{2}} \):
\[
\sqrt{5^{2} \times 8^{2}} = \sqrt{(5 \times 8)^{2}} = 5 \times 8 = 40
\]
(b) For \( \sqrt{4225} \):
\[
\sqrt{4225} = 65
\]
(c) For \( \sqrt{10609} \):
\[
\sqrt{10609} = 103
\]
Thus, the results are:
- (a) \( 40 \)
- (b) \( 65 \)
- (c) \( 103 \)
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Extra Insights
The first problem involves simplifying \( 5^{2} \times 8^{2} \). You can rewrite this expression using the property of square roots that states \( \sqrt{a \times b} = \sqrt{a} \times \sqrt{b} \). Thus, \( \sqrt{5^{2} \times 8^{2}} = \sqrt{(5 \times 8)^{2}} = 5 \times 8 = 40 \). For the second part, to find the square root of \( 4225 \), you can either use a calculator or identify perfect squares. Lucky for you, \( 65^2 = 4225 \), making \( \sqrt{4225} = 65 \). And for \( 10609 \), guess what? It's also a tidy perfect square! In fact, \( 103^2 = 10609 \), so \( \sqrt{10609} = 103 \). How fun is that?
