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liq [111]
4 years ago
10

" alt="\sqrt 45+\sqrt 20-\sqrt5\\" align="absmiddle" class="latex-formula">
Mathematics
1 answer:
allsm [11]4 years ago
8 0

Answer:

\mathbf{4\sqrt{5}=\sqrt{80}}

Step-by-step explanation:

one thing you should keep in mind while solving questions related to surds.

  • \mathit{\sqrt{a^{4} \cdot b}=\sqrt{a^{2}} \cdot \sqrt{a^{2}} \cdot \sqrt{b}=a \cdot a \cdot \sqrt{b}=a^{2}\sqrt{b}}
  • \mathit{\sqrt{a^{5}}=\sqrt{a^{2}} \cdot \sqrt{a^{2}} \cdot \sqrt{a}=a \cdot a \cdot \sqrt{a}=a^{2} \cdot \sqrt{a}}

from the above examples you can see that if you have a square of any number inside a square root then you can remove the square root and the square from that number or in other words you can take the number out of the square root.

Similarly in this question:

\sqrt{45}=\sqrt{9 \cdot 5}=\sqrt{3^{2} \cdot 5}=\sqrt{3^{2}} \cdot \sqrt{5}=3\sqrt{5}

\sqrt{20}=\sqrt{4 \cdot 5}=\sqrt{2^{2} \cdot 5}=\sqrt{2^{2}} \cdot \sqrt{5}=2\sqrt{5}

∴ \sqrt{45}+\sqrt{20}-\sqrt{5}=3 \cdot \sqrt{5}+2 \cdot \sqrt{5}-1 \cdot \sqrt{5}

Now take out \sqrt{5} common from all the terms of the above expression.

\sqrt{5} \cdot (3+2-1)=\sqrt{5} \cdot 4=4\sqrt{5}

In this you can send the terms back inside the square root. For example:

  • \mathit{a=\sqrt{a^{2}}}
  • \mathit{a^{3}\sqrt{b}=a \cdot a \cdot a \cdot \sqrt{b}=\sqrt{a^{2}} \cdot \sqrt{a^{2}} \cdot \sqrt{a^{2}} \cdot \sqrt{b}=\sqrt{a^{2} \cdot a^{2} \cdot a^{2} \cdot b}=\sqrt{a^{6}b}}

Similarly 4\sqrt{5}=\sqrt{4^{2} \cdot 5}=\sqrt{16 \cdot 5}=\sqrt{\mathbf{80}}

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Answer:

The numbers will remain the same.

Step-by-step explanation:

84.7 is already rounded to the nearest tenth because one digit to the right of the decimal is the tenths place.

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4 years ago
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Answer:

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Step-by-step explanation:

Given

12k² - 16k - 60 ← factor out 4 from each term

= 4(3k² - 4k - 15) ← factor the quadratic

Consider the factors of the product of the coefficient of the k² term and the constant term which sum to give the coefficient of the k term

product = 3 × - 15 = - 45 , sum = - 4

Factors are - 9 and + 5

Use these factors to split the middle term

3k² - 9k + 5k - 15 → ( factor the first/second and third/fourth terms

= 3k(k - 3) + 5(k - 3) ← factor out (k - 3)

= (k - 3)(3k + 5)

Hence

12k² - 16k - 60 = 4(k - 3)(3k + 5) ← in factored form

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Answer:

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Well hope all this helps :)

Step-by-step explanation:


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