Evaluate 4 + Square Root of 49 × 3: Order of Operations Practice

Q: Why can't I just work from left to right?

Mathematics has a specific order of operations (PEMDAS) that everyone must follow. Working left to right would give different people different answers for the same problem!

Q: Do square roots really come before multiplication?

Yes! Square roots are part of the "E" in PEMDAS (Exponents), which includes roots, powers, and other special operations. These come before multiplication and division.

Q: What if I get 33 as my answer?

Getting 33 means you added first: $ (4 + \sqrt{49}) \times 3 = (4 + 7) \times 3 = 11 \times 3 = 33 $. This violates PEMDAS! Always multiply before adding.

Q: How do I remember the correct order?

Use the acronym PEMDAS: Parentheses, Exponents (including square roots), Multiplication/Division, Addition/Subtraction. Work through each step carefully!

Q: Is there a way to double-check my work?

Yes! Write out each step: $ \sqrt{49} = 7 $, then $ 7 \times 3 = 21 $, finally $ 4 + 21 = 25 $. Each step should follow PEMDAS order.

Order of Operations with Square Roots

$4 + \sqrt{49} \times 3 =$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$4 + \sqrt{49} \times 3 =$

Step-by-step solution

First, solve the square root: $\sqrt{49} = 7$ .

Next, multiply 7 by 3: $7 \times 3 = 21$ .

Finally, add 4 to 21: $4 + 21 = 25$ .

Final Answer

$25$

Key Points to Remember

Essential concepts to master this topic

PEMDAS Rule: Square roots come before multiplication and addition operations
Technique: First $\sqrt{49} = 7$ , then multiply $7 \times 3 = 21$
Check: Follow PEMDAS step by step: $4 + \sqrt{49} \times 3 = 4 + 7 \times 3 = 4 + 21 = 25$ ✓

Common Mistakes

Avoid these frequent errors

Adding before multiplying
Don't calculate 4 + 7 = 11 first, then multiply by 3 = 33! This ignores the order of operations and gives the wrong answer. Always follow PEMDAS: solve the square root first, then multiply, then add.

Practice Quiz

Test your knowledge with interactive questions

What is the result of the following equation?

$36-4\div2$

FAQ

Everything you need to know about this question

Why can't I just work from left to right?

Mathematics has a specific order of operations (PEMDAS) that everyone must follow. Working left to right would give different people different answers for the same problem!

Do square roots really come before multiplication?

Yes! Square roots are part of the "E" in PEMDAS (Exponents), which includes roots, powers, and other special operations. These come before multiplication and division.

What if I get 33 as my answer?

Getting 33 means you added first: $(4 + \sqrt{49}) \times 3 = (4 + 7) \times 3 = 11 \times 3 = 33$ . This violates PEMDAS! Always multiply before adding.

How do I remember the correct order?

Use the acronym PEMDAS: Parentheses, Exponents (including square roots), Multiplication/Division, Addition/Subtraction. Work through each step carefully!

Is there a way to double-check my work?

Yes! Write out each step: $\sqrt{49} = 7$ , then $7 \times 3 = 21$ , finally $4 + 21 = 25$ . Each step should follow PEMDAS order.

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