Solve: 6 + Square Root of 64 - 4 Expression Evaluation

Q: Why do I have to do the square root first?

Square roots are exponent operations in PEMDAS/BODMAS, which come before addition and subtraction. Think of $ \sqrt{64} $ as $ 64^{1/2} $ - it's an exponent that must be calculated first!

Q: What if I forgot that √64 = 8?

Remember that perfect squares have nice whole number roots! Since $ 8 \times 8 = 64 $, we know $ \sqrt{64} = 8 $. Practice memorizing perfect squares from 1 to 144.

Q: Do I add and subtract from left to right or right to left?

Always work left to right for operations of equal priority! So 6 + 8 - 4 becomes: first 6 + 8 = 14, then 14 - 4 = 10.

Q: What would happen if I calculated 6 + 64 - 4 first?

You'd get 66, then $ \sqrt{66} $ ≈ 8.12, which is completely wrong! This breaks the order of operations and leads to the incorrect answer choice √66.

Q: How can I remember PEMDAS easily?

Try the phrase "Please Excuse My Dear Aunt Sally" for Parentheses, Exponents, Multiplication/Division, Addition/Subtraction. Square roots count as exponents!

Order of Operations with Square Roots

$6+\sqrt{64}-4=$

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Understand the problem

$6+\sqrt{64}-4=$

Step-by-step solution

To solve the expression $6+\sqrt{64}-4=$ , we need to follow the order of operations (PEMDAS/BODMAS):

P: Parentheses (or Brackets)
E: Exponents (or Orders, i.e., powers and roots, etc.)
MD: Multiplication and Division (left-to-right)
AS: Addition and Subtraction (left-to-right)

In this expression, we first need to evaluate the square root since it falls under the exponent category:

$\sqrt{64} = 8$

Next, we substitute the computed value back into the expression:

$6+8-4$

We then perform the addition and subtraction from left to right:

$6+8 = 14$

$14-4 = 10$

Thus, the final answer is:

$10$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Order Rule: Evaluate square roots before addition and subtraction operations
Technique: Calculate $\sqrt{64} = 8$ first, then solve 6 + 8 - 4
Check: Work left to right: 6 + 8 = 14, then 14 - 4 = 10 ✓

Common Mistakes

Avoid these frequent errors

Adding/subtracting before evaluating the square root
Don't calculate 6 + 64 - 4 = 66 first and then take the square root! This ignores order of operations and gives √66 instead of 10. Always evaluate square roots first, then perform addition and subtraction from left to right.

Practice Quiz

Test your knowledge with interactive questions

$7 + \sqrt{49} - 5 =$

FAQ

Everything you need to know about this question

Why do I have to do the square root first?

Square roots are exponent operations in PEMDAS/BODMAS, which come before addition and subtraction. Think of $\sqrt{64}$ as $64^{1/2}$ - it's an exponent that must be calculated first!

What if I forgot that √64 = 8?

Remember that perfect squares have nice whole number roots! Since $8 \times 8 = 64$ , we know $\sqrt{64} = 8$ . Practice memorizing perfect squares from 1 to 144.

Do I add and subtract from left to right or right to left?

Always work left to right for operations of equal priority! So 6 + 8 - 4 becomes: first 6 + 8 = 14, then 14 - 4 = 10.

What would happen if I calculated 6 + 64 - 4 first?

You'd get 66, then $\sqrt{66}$ ≈ 8.12, which is completely wrong! This breaks the order of operations and leads to the incorrect answer choice √66.

How can I remember PEMDAS easily?

Try the phrase "Please Excuse My Dear Aunt Sally" for Parentheses, Exponents, Multiplication/Division, Addition/Subtraction. Square roots count as exponents!

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