Answer :
Sure, let's find the square roots of the given fractions step-by-step:
### Part (i) [tex]\(\frac{25}{49}\)[/tex]
To find the square root of a fraction, we find the square root of the numerator and the denominator separately.
[tex]\[ \text{Numerator: } \sqrt{25} = 5 \][/tex]
[tex]\[ \text{Denominator: } \sqrt{49} = 7 \][/tex]
Thus, the square root of [tex]\(\frac{25}{49}\)[/tex] is [tex]\(\frac{5}{7}\)[/tex], or [tex]\((5.0, 7.0)\)[/tex] in decimal form.
### Part (ii) [tex]\(\frac{196}{484}\)[/tex]
Same process here, we find the square roots of the numerator and the denominator separately.
[tex]\[ \text{Numerator: } \sqrt{196} = 14 \][/tex]
[tex]\[ \text{Denominator: } \sqrt{484} = 22 \][/tex]
So, the square root of [tex]\(\frac{196}{484}\)[/tex] is [tex]\(\frac{14}{22}\)[/tex], or [tex]\((14.0, 22.0)\)[/tex] in decimal form.
### Part (iii) [tex]\(\frac{1225}{2025}\)[/tex]
Again, we calculate the square roots of both the numerator and the denominator.
[tex]\[ \text{Numerator: } \sqrt{1225} = 35 \][/tex]
[tex]\[ \text{Denominator: } \sqrt{2025} = 45 \][/tex]
Therefore, the square root of [tex]\(\frac{1225}{2025}\)[/tex] is [tex]\(\frac{35}{45}\)[/tex], or [tex]\((35.0, 45.0)\)[/tex] in decimal form.
### Part (iv) [tex]\(0.0009\)[/tex]
For decimal numbers, we directly find the square root of the number.
[tex]\[ \sqrt{0.0009} = 0.03 \][/tex]
### Part (v) [tex]\(0.00000049\)[/tex]
Similarly, we find the square root of the decimal number.
[tex]\[ \sqrt{0.00000049} = 0.0007 \][/tex]
### Summary
The square roots of the given fractions are as follows:
1. [tex]\(\frac{25}{49} \rightarrow (5.0, 7.0)\)[/tex]
2. [tex]\(\frac{196}{484} \rightarrow (14.0, 22.0)\)[/tex]
3. [tex]\(\frac{1225}{2025} \rightarrow (35.0, 45.0)\)[/tex]
4. [tex]\(0.0009 \rightarrow 0.03\)[/tex]
5. [tex]\(0.00000049 \rightarrow 0.0007\)[/tex]
These results are the final square roots of the provided fractions and decimal numbers.
### Part (i) [tex]\(\frac{25}{49}\)[/tex]
To find the square root of a fraction, we find the square root of the numerator and the denominator separately.
[tex]\[ \text{Numerator: } \sqrt{25} = 5 \][/tex]
[tex]\[ \text{Denominator: } \sqrt{49} = 7 \][/tex]
Thus, the square root of [tex]\(\frac{25}{49}\)[/tex] is [tex]\(\frac{5}{7}\)[/tex], or [tex]\((5.0, 7.0)\)[/tex] in decimal form.
### Part (ii) [tex]\(\frac{196}{484}\)[/tex]
Same process here, we find the square roots of the numerator and the denominator separately.
[tex]\[ \text{Numerator: } \sqrt{196} = 14 \][/tex]
[tex]\[ \text{Denominator: } \sqrt{484} = 22 \][/tex]
So, the square root of [tex]\(\frac{196}{484}\)[/tex] is [tex]\(\frac{14}{22}\)[/tex], or [tex]\((14.0, 22.0)\)[/tex] in decimal form.
### Part (iii) [tex]\(\frac{1225}{2025}\)[/tex]
Again, we calculate the square roots of both the numerator and the denominator.
[tex]\[ \text{Numerator: } \sqrt{1225} = 35 \][/tex]
[tex]\[ \text{Denominator: } \sqrt{2025} = 45 \][/tex]
Therefore, the square root of [tex]\(\frac{1225}{2025}\)[/tex] is [tex]\(\frac{35}{45}\)[/tex], or [tex]\((35.0, 45.0)\)[/tex] in decimal form.
### Part (iv) [tex]\(0.0009\)[/tex]
For decimal numbers, we directly find the square root of the number.
[tex]\[ \sqrt{0.0009} = 0.03 \][/tex]
### Part (v) [tex]\(0.00000049\)[/tex]
Similarly, we find the square root of the decimal number.
[tex]\[ \sqrt{0.00000049} = 0.0007 \][/tex]
### Summary
The square roots of the given fractions are as follows:
1. [tex]\(\frac{25}{49} \rightarrow (5.0, 7.0)\)[/tex]
2. [tex]\(\frac{196}{484} \rightarrow (14.0, 22.0)\)[/tex]
3. [tex]\(\frac{1225}{2025} \rightarrow (35.0, 45.0)\)[/tex]
4. [tex]\(0.0009 \rightarrow 0.03\)[/tex]
5. [tex]\(0.00000049 \rightarrow 0.0007\)[/tex]
These results are the final square roots of the provided fractions and decimal numbers.
