Solve: 4×sqrt(0.49) + 4² | Mixed Operations Expression

Q: Why do I calculate the square root before multiplying by 4?

Because of the order of operations (PEMDAS)! Roots and exponents come before multiplication and division. So you must find $ \sqrt{0.49} = 0.7 $ first, then multiply: $ 4 \times 0.7 = 2.8 $.

Q: How do I find the square root of 0.49?

Think: what number times itself equals 0.49? Since $ 0.7 \times 0.7 = 0.49 $, we know $ \sqrt{0.49} = 0.7 $. You can also recognize that 0.49 = 49/100, so $ \sqrt{0.49} = \sqrt{49}/\sqrt{100} = 7/10 = 0.7 $.

Q: What if I calculated 4² as 8 instead of 16?

Double-check exponents! $ 4^2 $ means 4 × 4 = 16, not 4 × 2 = 8. The small 2 tells you to multiply 4 by itself, not by 2.

Q: Can I use a calculator for the square root?

Yes! But try to recognize common square roots like $ \sqrt{0.25} = 0.5 $, $ \sqrt{0.49} = 0.7 $, and $ \sqrt{0.81} = 0.9 $. This builds your number sense!

Q: Why is the final answer 18.8 and not 19?

Because we're working with exact values! $ 4 \times 0.7 = 2.8 $ exactly, and $ 2.8 + 16 = 18.8 $ exactly. Never round until the very end unless the problem asks you to.

Order of Operations with Square Roots

$4\times\sqrt{0.49}+4^2=$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:07 Let's solve this expression together.

00:11 First, we'll break down zero point four nine into zero point seven squared.

00:17 Remember, the square root of a squared number cancels out the square.

00:22 Always solve multiplication and division before tackling addition and subtraction.

00:29 Use vertical multiplication to find the product easily.

00:37 And remember, any number multiplied by zero is always zero.

00:50 Be aware of where you place the decimal point.

00:55 Now, continue solving the expression step by step.

00:59 Great job! That's how you find the solution.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$4\times\sqrt{0.49}+4^2=$

Step-by-step solution

To solve the expression $4\times\sqrt{0.49}+4^2 =$ , we will follow the order of operations, which prioritizes operations inside parentheses, exponents and roots, followed by multiplication and division, and finally addition and subtraction.

1. Calculate the Square Root:
The first step is to solve the square root part of the expression. $\sqrt{0.49}$ .
$0.49$ is a simple decimal number whose square root is $0.7$ , because $0.7 \times 0.7 = 0.49$ .
So, $\sqrt{0.49} = 0.7$ .

2. Multiply:
Next, we multiply the result of the square root by 4:
$4 \times 0.7 = 2.8$ .

3. Calculate the Power:
Evaluate $4^2$ .
$4^2 = 16$ , because $4 \times 4 = 16$ .

4. Addition:
Now, add the results from the previous steps:
$2.8 + 16 = 18.8$ .

The final result of the expression $4\times\sqrt{0.49}+4^2$ is $\boxed{18.8}$ .

Final Answer

18.8

Key Points to Remember

Essential concepts to master this topic

Order Rule: Follow PEMDAS - roots first, then multiplication, then addition
Technique: Calculate $\sqrt{0.49} = 0.7$ , then $4 \times 0.7 = 2.8$
Check: Verify each step: 0.7 × 0.7 = 0.49, then 2.8 + 16 = 18.8 ✓

Common Mistakes

Avoid these frequent errors

Adding before completing all operations
Don't add 0.49 + 16 = 16.49 first! This ignores the square root and multiplication. The order of operations requires you to complete roots and multiplication before addition. Always follow PEMDAS: calculate $\sqrt{0.49}$ first, then multiply by 4, then add $4^2$ .

Practice Quiz

Test your knowledge with interactive questions

$\sqrt{4}=$

FAQ

Everything you need to know about this question

Why do I calculate the square root before multiplying by 4?

Because of the order of operations (PEMDAS)! Roots and exponents come before multiplication and division. So you must find $\sqrt{0.49} = 0.7$ first, then multiply: $4 \times 0.7 = 2.8$ .

How do I find the square root of 0.49?

Think: what number times itself equals 0.49? Since $0.7 \times 0.7 = 0.49$ , we know $\sqrt{0.49} = 0.7$ . You can also recognize that 0.49 = 49/100, so $\sqrt{0.49} = \sqrt{49}/\sqrt{100} = 7/10 = 0.7$ .

What if I calculated 4² as 8 instead of 16?

Double-check exponents! $4^2$ means 4 × 4 = 16, not 4 × 2 = 8. The small 2 tells you to multiply 4 by itself, not by 2.

Can I use a calculator for the square root?

Yes! But try to recognize common square roots like $\sqrt{0.25} = 0.5$ , $\sqrt{0.49} = 0.7$ , and $\sqrt{0.81} = 0.9$ . This builds your number sense!

Why is the final answer 18.8 and not 19?

Because we're working with exact values! $4 \times 0.7 = 2.8$ exactly, and $2.8 + 16 = 18.8$ exactly. Never round until the very end unless the problem asks you to.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Powers and Roots - Basic questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

Solve: 4×sqrt(0.49) + 4² | Mixed Operations Expression

Order of Operations with Square Roots

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why do I calculate the square root before multiplying by 4?

How do I find the square root of 0.49?

What if I calculated 4² as 8 instead of 16?

Can I use a calculator for the square root?

Why is the final answer 18.8 and not 19?

🌟 Unlock Your Math Potential

More Questions

Powers and Roots

Solve: 7 + √49 - 5 | Square Root and Basic Operations

Solve 3 × 2 + √81: Order of Operations with Square Root

Solve 143 - Square Root of 121 + 18: Complete Expression Evaluation

Solve (√380.25 - ½)² - 11: Complete Square Root Expression

Square Roots

Solve: 81 + Square Root of 81 + 10 Expression

Evaluate 5 + Square Root of 36 - 1: Step-by-Step Solution