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Calculate. (a) $(6^2 + 5)^3$ (b) $\sqrt{\frac{8.4^2 - 1.9^2}{2.5 + 5.7}}$ Write your answer correct to 3 significant figures. - OCR - GCSE Maths - Question 1 - 2021 - Paper 1

Question 1

$Calculate.-(a)-$(6^2-+-5)^3$--(b)-$\sqrt{\frac{8.4^2---1.9^2}{2.5-+-5.7}}$--Write-your-answer-correct-to-3-significant-figures.-OCR-GCSE Maths-Question 1-2021-Paper 1.png$

Calculate. (a) $(6^2 + 5)^3$ (b) $\sqrt{\frac{8.4^2 - 1.9^2}{2.5 + 5.7}}$ Write your answer correct to 3 significant figures.

Worked Solution & Example Answer:Calculate. (a) $(6^2 + 5)^3$ (b) $\sqrt{\frac{8.4^2 - 1.9^2}{2.5 + 5.7}}$ Write your answer correct to 3 significant figures. - OCR - GCSE Maths - Question 1 - 2021 - Paper 1

Step 1

(a) $(6^2 + 5)^3$

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Answer

To solve the expression, we first calculate inside the parentheses:

Calculate $6^2$ : $6^2 = 36$
Add 5: $36 + 5 = 41$
Now cube the result: $41^3 = 41 \times 41 \times 41 = 68921$

Thus, the answer for part (a) is 68921.

Step 2

(b) $\sqrt{\frac{8.4^2 - 1.9^2}{2.5 + 5.7}}$

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Answer

To solve this expression, follow these steps:

Calculate $8.4^2$ : $8.4^2 = 70.56$
Calculate $1.9^2$ : $1.9^2 = 3.61$
Subtract the squares: $70.56 - 3.61 = 66.95$
Add the denominator values: $2.5 + 5.7 = 8.2$
Calculate the fraction: $\frac{66.95}{8.2} \approx 8.16$
Take the square root: $\sqrt{8.16} \approx 2.8579$

Finally, round the answer to 3 significant figures: $2.86$

Thus, the answer for part (b) is 2.86.

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