Can you solve 5 × √196 without a calculator? First find the square root of 196, then multiply the result by 5. Since √196 = 14, the final answer is 70.
This kind of problem combines a square root with multiplication. The best strategy is to simplify the square root first, then complete the multiplication. The video also shows a quick digit-sum clue that helps you recognize 14.
The Quick Answer: 5 × √196 = 70
Break the problem into two simple steps:
Step 1: Find √196
To find √196, ask: What number multiplied by itself equals 196?
Therefore:
Step 2: Multiply by 5
Now replace √196 with 14 and multiply:
So the final answer is:
The Video’s Quick Digit-Sum Clue
The video uses a memorable pattern to reach 14 from the digits in 196:
Then subtract 2:
This gives the square-root candidate 14. Always confirm it by squaring:
After that verification, multiply by 5:
Why Simplify the Square Root First?
Multiplication and square-root operations can be handled in an efficient order when the number under the radical is a perfect square:
Trying to estimate √196 before multiplying can make the problem harder. Simplifying first turns the radical expression into an ordinary multiplication problem.
Use Nearby Perfect Squares
If you do not remember that 14² = 196, compare 196 with nearby perfect squares:
| Number | Square | Comparison with 196 |
|---|---|---|
| 13 | 13² = 169 | Too small |
| 14 | 14² = 196 | Exact match |
| 15 | 15² = 225 | Too large |
The exact match is 14² = 196, so √196 = 14.
More Examples with the Same Method
Use the same two-step process: simplify the square root, then multiply by the number outside the radical.
Common Mistakes to Avoid
Do not multiply 5 by 196 and then take the square root. The expression is 5 × √196, so simplify the square root first:
Do not forget that √196 means the principal, nonnegative square root. Therefore √196 = 14. If you solve x² = 196, the two solutions are x = 14 and x = −14.
Finally, treat the digit-sum method as a quick clue rather than a universal square-root formula. The exact proof is the verification 14 × 14 = 196.
Practice Problems
Simplify the square root first, then complete the multiplication:
- 2 × √100
- 3 × √121
- 5 × √256
- 4 × √361
- 7 × √400
Answer Key
- 2 × √100 = 2 × 10 = 20
- 3 × √121 = 3 × 11 = 33
- 5 × √256 = 5 × 16 = 80
- 4 × √361 = 4 × 19 = 76
- 7 × √400 = 7 × 20 = 140
Final Takeaway
For a problem such as 5 × √196, simplify the square root before multiplying:
The video’s quick clue is:
Then confirm the result with 14² = 196. This combination of a fast pattern and exact verification makes square-root multiplication easier for homework, quizzes, and mental-math practice.
Frequently Asked Questions
What is 5 × √196?
5 × √196 equals 70, because √196 = 14 and 5 × 14 = 70.
How do you find √196?
Find the number that squares to 196. Since 14 × 14 = 196, √196 = 14.
What digit-sum trick does the video show?
The video adds the digits 1 + 9 + 6 = 16, then subtracts 2 to reach 14. This is a pattern clue for the example and should be checked using 14² = 196.
Can the square root be simplified before multiplication?
Yes. When the number under the radical is a perfect square, simplify it first. For example, 5 × √196 becomes 5 × 14 = 70.
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