Answer :
To determine between which two integers the square root of 46 lies, we can follow these steps:
1. Estimate the Square Roots of Nearby Perfect Squares:
- First, identify perfect squares that are close to 46. These are numbers whose square roots are whole numbers.
- The perfect squares close to 46 are 36 (since [tex]\(6^2 = 36\)[/tex]) and 49 (since [tex]\(7^2 = 49\)[/tex]).
2. Identify the Integers Related to These Perfect Squares:
- The square root of 36 is 6, and the square root of 49 is 7.
3. Approximate [tex]\(\sqrt{46}\)[/tex]:
- Since 46 is between 36 and 49, and given that the square root of 46 will also be between the square roots of these two perfect squares, we know [tex]\(\sqrt{46}\)[/tex] will lie between 6 and 7.
- Specifically, [tex]\(6 < \sqrt{46} < 7\)[/tex].
4. Final Conclusion:
- Therefore, [tex]\(\sqrt{46}\)[/tex] lies between the integers 6 and 7.
This step-by-step reasoning shows that [tex]\(\sqrt{46}\)[/tex] is indeed located between the integers 6 and 7.
1. Estimate the Square Roots of Nearby Perfect Squares:
- First, identify perfect squares that are close to 46. These are numbers whose square roots are whole numbers.
- The perfect squares close to 46 are 36 (since [tex]\(6^2 = 36\)[/tex]) and 49 (since [tex]\(7^2 = 49\)[/tex]).
2. Identify the Integers Related to These Perfect Squares:
- The square root of 36 is 6, and the square root of 49 is 7.
3. Approximate [tex]\(\sqrt{46}\)[/tex]:
- Since 46 is between 36 and 49, and given that the square root of 46 will also be between the square roots of these two perfect squares, we know [tex]\(\sqrt{46}\)[/tex] will lie between 6 and 7.
- Specifically, [tex]\(6 < \sqrt{46} < 7\)[/tex].
4. Final Conclusion:
- Therefore, [tex]\(\sqrt{46}\)[/tex] lies between the integers 6 and 7.
This step-by-step reasoning shows that [tex]\(\sqrt{46}\)[/tex] is indeed located between the integers 6 and 7.
