Question

given that √ 1.530 169 = 1237 find the value of
a) √1.530169 + √153.0169
b)√15301.69 + √1.530169
please anwer it
​

Answer 1

Answer:

1.530 ‎169 =

Step-by-step explanation:

Answer 2

$\underline{ \underline{ \Large \sf { \pink{Given:}} } }$

• $\sf { \sqrt{1530169} = 1237 }$

⠀⠀⠀⠀⠀⠀___________

$\underline{ \underline{ \Large \sf { \purple{To \: calculate:}} } }$

• $\sf { \sqrt{1.530169} +\sqrt{153.0169} }$

• $\sf { \sqrt{15301.69} \div \sqrt{1.530169} }$

⠀⠀⠀⠀⠀⠀___________

$\underline{ \underline{ \Large \sf { \pink{Calculation:}} } }$

Solution (a) :

✰$\sf { \sqrt{1.530169} +\sqrt{153.0169} }$

Firstly, we'll write the following numbers having decimals into fractions to easily simplify this.

$\longrightarrow \sf { \sqrt{\dfrac{1530169}{1000000}} +\sqrt{ \dfrac{1530169}{10000} }}$

Now, by using one of the idendties of square roots, that is :

• $\sf {\sqrt{\dfrac{a}{b}} = \dfrac{\sqrt{a}}{\sqrt{b} }}$

$\longrightarrow \sf { \dfrac{\sqrt{1530169}}{\sqrt{1000000} } +\dfrac{\sqrt{1530169}}{\sqrt{10000} } }$

Here, we are already given the value of $\sf { \sqrt{1530169} }$ that is 1237. We have to find the value of √1000000 & √10000. By prime factorization,

⇒ 1000000 = 10 × 10 × 10 × 10 × 10 × 10

⇒ √1000000 = 10 × 10 × 10 × 10 × 10 × 10

⇒ √1000000 = 10 × 10 × 10

⇒ √1000000 = 1000

Also,

⇒ 10000 = 100 × 100

⇒ √10000 = √( 100 × 100 )

⇒ √10000 = √100 × √100

⇒ √10000 = 10 × 10

⇒ √10000 = 100

So,

$\longrightarrow \sf { \dfrac{1237}{1000} +\dfrac{1237}{100} }$

Now, writing it into decimal form and performing addition.

$\longrightarrow \sf { 1.237 + 12.37}$

$\longrightarrow \sf { 13.607}$

Henceforth,

$\to \sf { \sqrt{1.530169} +\sqrt{153.0169} = \pmb {\mathfrak \gray{13.607} } }$

⠀⠀⠀⠀⠀⠀____________

✰ $\sf { \sqrt{15301.69} \div \sqrt{1.530169} }$

Firstly, we'll write the following numbers having decimals into fractions to easily simplify this.

$\longrightarrow \sf {\sqrt{ \dfrac{1530169}{100} }\div \sqrt{ \dfrac{1530169}{1000000}} }$

Now, by using one of the idendties of square roots, that is :

• $\sf {\sqrt{\dfrac{a}{b}} = \dfrac{\sqrt{a}}{\sqrt{b} }}$

$\longrightarrow \sf { \dfrac{\sqrt{1530169}}{\sqrt{100} } \div \dfrac{\sqrt{1530169}}{\sqrt{1000000} } }$

Here, we are already given the value of $\sf { \sqrt{1530169} }$ that is 1237. We have to find the value of √100 & √1000000. By prime factorization,

⇒ 100 = 10 × 10

⇒ √100 = √(10 × 10)

⇒ √100 = √$\sf {{ 10}^{2} }$

⇒ √100 = 10

Also,

⇒ 1000000 = 10 × 10 × 10 × 10 × 10 × 10

⇒ √1000000 = 10 × 10 × 10 × 10 × 10 × 10

⇒ √1000000 = 10 × 10 × 10

⇒ √1000000 = 1000

So,

$\longrightarrow \sf { \dfrac{1237}{10} \div \dfrac{1237}{100} }$

By using fraction rule,

• $\sf { \dfrac{A}{B} \div \dfrac{C}{D} = \dfrac{AD}{BC} }$

$\longrightarrow \sf { \dfrac{\cancel{1237}}{\cancel{10}} \times \dfrac{\cancel{1000}}{\cancel{1237}} }$

$\longrightarrow \sf {100 }$

Henceforth,

$\to \sf { \sqrt{15301.69} +\sqrt{1.530169} = \pmb {\mathfrak \gray{100} } }$

⠀⠀⠀⠀⠀⠀____________