Solve: Square Root Product (√9 × √4) Plus 9² × 6 Expression

Order of Operations with Square Roots

9×4+92×6= \sqrt{9}\times\sqrt{4}+9^2\times6=

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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 Calculate the roots
00:17 Calculate the exponent
00:20 Always solve multiplication and division before addition and subtraction
00:26 Calculate each multiplication and then add
00:33 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

9×4+92×6= \sqrt{9}\times\sqrt{4}+9^2\times6=

2

Step-by-step solution

Let's solve the following expression step by step using the order of operations: 9×4+92×6= \sqrt{9}\times\sqrt{4}+9^2\times6= .

1. Calculate the square roots:
- The square root of 9 is 3, so 9=3 \sqrt{9} = 3 .
- The square root of 4 is 2, so 4=2 \sqrt{4} = 2 .
Thus, the expression becomes 3×2+92×6 3 \times 2 + 9^2 \times 6 .

2. Multiplication of the square roots:
- Multiply the results of the square roots: 3×2=6 3 \times 2 = 6 .

3. Calculate the power:
- Calculate 9 squared: 92=81 9^2 = 81 .

4. Multiply with 6:
- Multiply the power result by 6: 81×6=486 81 \times 6 = 486 .

5. Final addition:
- Add the result from the square roots and the power: 6+486=492 6 + 486 = 492 .

The evaluated result of the expression 9×4+92×6 \sqrt{9}\times\sqrt{4}+9^2\times6 is 492

3

Final Answer

492

Key Points to Remember

Essential concepts to master this topic
  • PEMDAS Rule: Calculate square roots and powers before multiplication and addition
  • Technique: 9=3 \sqrt{9} = 3 and 92=81 9^2 = 81 before multiplying by other numbers
  • Check: Final calculation should be 6+486=492 6 + 486 = 492

Common Mistakes

Avoid these frequent errors
  • Adding before completing all multiplications
    Don't calculate 3×2+92 3 \times 2 + 9^2 as (3×2+9)2×6=900 (3 \times 2 + 9)^2 \times 6 = 900 ! This ignores order of operations and gives completely wrong results. Always complete all exponents, then all multiplications, then addition last.

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

Do I calculate the square roots first or the exponent first?

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Both square roots and exponents have equal priority in PEMDAS! Calculate them from left to right: first 9=3 \sqrt{9} = 3 and 4=2 \sqrt{4} = 2 , then 92=81 9^2 = 81 .

Can I multiply the square roots together using the rule a×b=ab \sqrt{a} \times \sqrt{b} = \sqrt{ab} ?

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Yes, absolutely! You can calculate 9×4=36=6 \sqrt{9} \times \sqrt{4} = \sqrt{36} = 6 . This gives the same result as 3×2=6 3 \times 2 = 6 , so use whichever method feels easier!

Why do I get 492 instead of a smaller number?

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The large result comes from 92×6=81×6=486 9^2 \times 6 = 81 \times 6 = 486 ! Remember that squaring makes numbers much bigger, and then multiplying by 6 makes it even larger. The square roots only contribute 6 to the total.

What if I calculated 92×6 9^2 \times 6 as 9×(2×6) 9 \times (2 \times 6) ?

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That's wrong! The expression 92 9^2 means 9×9=81 9 \times 9 = 81 , not 9×2 9 \times 2 . Always calculate exponents first before any other operations.

How can I double-check my arithmetic?

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Break it into parts: 9×4=6 \sqrt{9} \times \sqrt{4} = 6 , then 92=81 9^2 = 81 , then 81×6=486 81 \times 6 = 486 , finally 6+486=492 6 + 486 = 492 . Each step should be simple mental math!

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