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

What is the result of the following equation?

$36-4\div2$

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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