What is the value of ( \sqrt{80}\div\sqrt{5} )?
Answer and explanation
Correct answer: (4)
The quotient of square roots can be simplified by using \\(\frac{\sqrt{a}}{\sqrt{b}}=\sqrt{\frac{a}{b}}\\) when the denominator is positive. Here, both 80 and 5 are positive, so the rule applies directly. Dividing the numbers inside the radical gives \\(\sqrt{80}\div\sqrt{5}=\sqrt{\frac{80}{5}}=\sqrt{16}\\).
The square root of 16 is 4 because \\(4\times4=16\\). Therefore, option A is correct. Another valid route is to write \\(\sqrt{80}=\sqrt{16\times5}=4\sqrt{5}\\), and then divide by \\(\sqrt{5}\\), again obtaining 4. The other numerical choices result from incorrect treatment of the square roots.
Frequently asked questions
What is the correct answer to this question?
(4)
Why is this the correct answer?
The quotient of square roots can be simplified by using \\(\frac{\sqrt{a}}{\sqrt{b}}=\sqrt{\frac{a}{b}}\\) when the denominator is positive. Here, both 80 and 5 are positive, so the rule applies directly. Dividing the numbers inside the radical gives \\(\sqrt{80}\div\sqrt{5}=\sqrt{\frac{80}{5}}=\sqrt{16}\\).
The square root of 16 is 4 because \\(4\times4=16\\). Therefore, option A is correct. Another valid route is to write \\(\sqrt{80}=\sqrt{16\times5}=4\sqrt{5}\\), and then divide by \\(\sqrt{5}\\), again obtaining 4. The other numerical choices result from incorrect treatment of the square roots.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Real Numbers.
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