Simplify the Expression: √121/11 - Step-by-Step Solution

Q: How do I know that √121 equals 11?

Think: what number times itself equals 121? Since 11 × 11 = 121, we know $ \sqrt{121} = 11 $. Perfect squares like 121 always have whole number square roots!

Q: Why don't I divide 121 by 11 first?

Order of operations matters! The square root symbol acts like parentheses - you must calculate $ \sqrt{121} $ first, then divide by 11. Think of it as $ \frac{(\sqrt{121})}{11} $.

Q: What if I can't remember if 121 is a perfect square?

Try counting up: $ 10^2 = 100 $, $ 11^2 = 121 $, $ 12^2 = 144 $. Or use the pattern: 121 ends in 1, and numbers ending in 1 squared also end in 1!

Q: What would happen if the denominator was different?

The answer would change! For example, $ \frac{\sqrt{121}}{22} = \frac{11}{22} = \frac{1}{2} $. Always calculate the square root first, then perform the division.

Square Roots with Perfect Square Division

Complete the following exercise:

$\frac{\sqrt{121}}{11}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve the following problem

00:03 Determine which number multiplied by itself equals 121

00:12 Break down 121 into 11 squared

00:21 The square root of any number (A) squared cancels out the square

00:25 Apply this formula to our exercise

00:31 Any number divided by itself always equals 1

00:34 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Complete the following exercise:

$\frac{\sqrt{121}}{11}=$

Step-by-step solution

To solve the problem, we'll take the following steps:

Compute the square root of the number 121.
Divide the square root result by 11.

Let's go through the calculations:

First, compute the square root of 121:

$\sqrt{121} = 11$

Next, divide this result by 11:

$\frac{11}{11} = 1$

Thus, the value of $\frac{\sqrt{121}}{11}$ is $1$ .

Therefore, the correct answer is choice 1, which corresponds to 1.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Perfect Square Recognition: Identify that 121 equals 11 × 11
Square Root Calculation: $\sqrt{121} = 11$ since 11² = 121
Verification Check: Substitute back: $\frac{11}{11} = 1$ ✓

Common Mistakes

Avoid these frequent errors

Dividing 121 by 11 before taking the square root
Don't calculate $\frac{121}{11} = 11$ first then take the square root = wrong order of operations! This gives $\sqrt{11}$ instead of 1. Always follow order of operations: calculate the square root first, then divide.

Practice Quiz

Test your knowledge with interactive questions

Solve the following exercise:

$\sqrt{\frac{2}{4}}=$

FAQ

Everything you need to know about this question

How do I know that √121 equals 11?

Think: what number times itself equals 121? Since 11 × 11 = 121, we know $\sqrt{121} = 11$ . Perfect squares like 121 always have whole number square roots!

Why don't I divide 121 by 11 first?

Order of operations matters! The square root symbol acts like parentheses - you must calculate $\sqrt{121}$ first, then divide by 11. Think of it as $\frac{(\sqrt{121})}{11}$ .

What if I can't remember if 121 is a perfect square?

Try counting up: $10^2 = 100$ , $11^2 = 121$ , $12^2 = 144$ . Or use the pattern: 121 ends in 1, and numbers ending in 1 squared also end in 1!

Can this fraction be simplified further?

No, the answer is simply 1. When any non-zero number is divided by itself, the result is always 1. Since $\sqrt{121} = 11$ , we get $\frac{11}{11} = 1$ .

What would happen if the denominator was different?

The answer would change! For example, $\frac{\sqrt{121}}{22} = \frac{11}{22} = \frac{1}{2}$ . Always calculate the square root first, then perform the division.

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