Math

QuestionIdentify the irrational number from the options: a. 3969\sqrt{3969}, b. 2892500\frac{\sqrt{289}}{2500}, c. 289250\sqrt{\frac{289}{250}}, d. 9801\sqrt{9801}.

Studdy Solution

STEP 1

Assumptions1. An irrational number cannot be expressed as a ratio of two integers. . The square root of a perfect square is a rational number.
3. The division of two rational numbers is a rational number.

STEP 2

First, let's check option a. We need to find the square root of3969.
3969\sqrt{3969}

STEP 3

Calculate the square root of3969.
3969=63\sqrt{3969} =63Since63 is a rational number, option a is not the answer.

STEP 4

Next, let's check option b. We need to find the square root of289 and divide it by2500.
2892500\frac{\sqrt{289}}{2500}

STEP 5

Calculate the square root of289 and divide it by2500.
2892500=172500\frac{\sqrt{289}}{2500} = \frac{17}{2500}Since 172500\frac{17}{2500} is a rational number, option b is not the answer.

STEP 6

Next, let's check option c. We need to find the square root of 289250\frac{289}{250}.
289250\sqrt{\frac{289}{250}}

STEP 7

Calculate the square root of 289250\frac{289}{250}.
289250=1.156\sqrt{\frac{289}{250}} = \sqrt{1.156}This number is not a perfect square, so it's possible that this could be an irrational number. We'll need to check the last option to be sure.

STEP 8

Finally, let's check option d. We need to find the square root of9801.
9801\sqrt{9801}

STEP 9

Calculate the square root of980.
980=99\sqrt{980} =99Since99 is a rational number, option d is not the answer.

STEP 10

After checking all the options, we find that the only option that could possibly be an irrational number is option c.
289250=.156\sqrt{\frac{289}{250}} = \sqrt{.156}This is because the square root of a non-perfect square is an irrational number.
So, the number that is irrational is 289250\sqrt{\frac{289}{250}}.

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