Westonci.ca is the ultimate Q&A platform, offering detailed and reliable answers from a knowledgeable community. Experience the ease of finding accurate answers to your questions from a knowledgeable community of professionals. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.
Sagot :
Let's evaluate each of the given expressions step-by-step:
### (a) [tex]\(\sqrt{1 \frac{49}{576}}\)[/tex]
First, convert the mixed number [tex]\(1 \frac{49}{576}\)[/tex] into an improper fraction.
1 + [tex]\(\frac{49}{576}\)[/tex] is the same as:
[tex]\[ 1 + \frac{49}{576} = \frac{576}{576} + \frac{49}{576} = \frac{576 + 49}{576} = \frac{625}{576} \][/tex]
Now, take the square root of [tex]\(\frac{625}{576}\)[/tex]:
[tex]\[ \sqrt{\frac{625}{576}} = \frac{\sqrt{625}}{\sqrt{576}} = \frac{25}{24} \][/tex]
Thus, the result is approximately [tex]\(1.0416666666666667\)[/tex].
### (b) [tex]\(\sqrt{1 \frac{56}{169}}\)[/tex]
Convert the mixed number [tex]\(1 \frac{56}{169}\)[/tex] into an improper fraction:
[tex]\[ 1 + \frac{56}{169} = \frac{169}{169} + \frac{56}{169} = \frac{169 + 56}{169} = \frac{225}{169} \][/tex]
Now, take the square root of [tex]\(\frac{225}{169}\)[/tex]:
[tex]\[ \sqrt{\frac{225}{169}} = \frac{\sqrt{225}}{\sqrt{169}} = \frac{15}{13} \][/tex]
Thus, the result is approximately [tex]\(1.1538461538461537\)[/tex].
### (c) [tex]\(\sqrt{2 \frac{1}{4}}\)[/tex]
Convert the mixed number [tex]\(2 \frac{1}{4}\)[/tex] into an improper fraction:
[tex]\[ 2 + \frac{1}{4} = \frac{8}{4} + \frac{1}{4} = \frac{9}{4} \][/tex]
Now, take the square root of [tex]\(\frac{9}{4}\)[/tex]:
[tex]\[ \sqrt{\frac{9}{4}} = \frac{\sqrt{9}}{\sqrt{4}} = \frac{3}{2} \][/tex]
Thus, the result is [tex]\(1.5\)[/tex].
### (d) [tex]\(\sqrt{\frac{1}{16} + \frac{1}{9}}\)[/tex]
First, find a common denominator for [tex]\(\frac{1}{16}\)[/tex] and [tex]\(\frac{1}{9}\)[/tex]. The least common denominator of 16 and 9 is 144:
[tex]\[ \frac{1}{16} = \frac{9}{144}, \quad \frac{1}{9} = \frac{16}{144} \][/tex]
Add the fractions:
[tex]\[ \frac{1}{16} + \frac{1}{9} = \frac{9}{144} + \frac{16}{144} = \frac{25}{144} \][/tex]
Now, take the square root of [tex]\(\frac{25}{144}\)[/tex]:
[tex]\[ \sqrt{\frac{25}{144}} = \frac{\sqrt{25}}{\sqrt{144}} = \frac{5}{12} \][/tex]
Thus, the result is approximately [tex]\(0.4166666666666667\)[/tex].
In summary, the evaluated results are:
- (a) [tex]\(1.0416666666666667\)[/tex]
- (b) [tex]\(1.1538461538461537\)[/tex]
- (c) [tex]\(1.5\)[/tex]
- (d) [tex]\(0.4166666666666667\)[/tex]
### (a) [tex]\(\sqrt{1 \frac{49}{576}}\)[/tex]
First, convert the mixed number [tex]\(1 \frac{49}{576}\)[/tex] into an improper fraction.
1 + [tex]\(\frac{49}{576}\)[/tex] is the same as:
[tex]\[ 1 + \frac{49}{576} = \frac{576}{576} + \frac{49}{576} = \frac{576 + 49}{576} = \frac{625}{576} \][/tex]
Now, take the square root of [tex]\(\frac{625}{576}\)[/tex]:
[tex]\[ \sqrt{\frac{625}{576}} = \frac{\sqrt{625}}{\sqrt{576}} = \frac{25}{24} \][/tex]
Thus, the result is approximately [tex]\(1.0416666666666667\)[/tex].
### (b) [tex]\(\sqrt{1 \frac{56}{169}}\)[/tex]
Convert the mixed number [tex]\(1 \frac{56}{169}\)[/tex] into an improper fraction:
[tex]\[ 1 + \frac{56}{169} = \frac{169}{169} + \frac{56}{169} = \frac{169 + 56}{169} = \frac{225}{169} \][/tex]
Now, take the square root of [tex]\(\frac{225}{169}\)[/tex]:
[tex]\[ \sqrt{\frac{225}{169}} = \frac{\sqrt{225}}{\sqrt{169}} = \frac{15}{13} \][/tex]
Thus, the result is approximately [tex]\(1.1538461538461537\)[/tex].
### (c) [tex]\(\sqrt{2 \frac{1}{4}}\)[/tex]
Convert the mixed number [tex]\(2 \frac{1}{4}\)[/tex] into an improper fraction:
[tex]\[ 2 + \frac{1}{4} = \frac{8}{4} + \frac{1}{4} = \frac{9}{4} \][/tex]
Now, take the square root of [tex]\(\frac{9}{4}\)[/tex]:
[tex]\[ \sqrt{\frac{9}{4}} = \frac{\sqrt{9}}{\sqrt{4}} = \frac{3}{2} \][/tex]
Thus, the result is [tex]\(1.5\)[/tex].
### (d) [tex]\(\sqrt{\frac{1}{16} + \frac{1}{9}}\)[/tex]
First, find a common denominator for [tex]\(\frac{1}{16}\)[/tex] and [tex]\(\frac{1}{9}\)[/tex]. The least common denominator of 16 and 9 is 144:
[tex]\[ \frac{1}{16} = \frac{9}{144}, \quad \frac{1}{9} = \frac{16}{144} \][/tex]
Add the fractions:
[tex]\[ \frac{1}{16} + \frac{1}{9} = \frac{9}{144} + \frac{16}{144} = \frac{25}{144} \][/tex]
Now, take the square root of [tex]\(\frac{25}{144}\)[/tex]:
[tex]\[ \sqrt{\frac{25}{144}} = \frac{\sqrt{25}}{\sqrt{144}} = \frac{5}{12} \][/tex]
Thus, the result is approximately [tex]\(0.4166666666666667\)[/tex].
In summary, the evaluated results are:
- (a) [tex]\(1.0416666666666667\)[/tex]
- (b) [tex]\(1.1538461538461537\)[/tex]
- (c) [tex]\(1.5\)[/tex]
- (d) [tex]\(0.4166666666666667\)[/tex]
Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.
