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

\( 5+\sqrt{36}-1= \)

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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