Name: Estimation of Square Roots
Uploaded: 2019-07-19
Duration: 6 min 2 s
Description: For not-perfect squares, we can estimate their square root to the closest whole number. Learn how to estimate the square root of non-perfect squares.

Question

Simplify:

[\sqrt{729} + \sqrt[3]{0.729} + \sqrt{0.0729}] \times \sqrt{\frac{1}{729}}

Accepted Answer

Given, $[\sqrt{729} + \sqrt[3]{0.729} + \sqrt{0.0729}] \times \sqrt{\frac{1}{729}}$

Covert decimals into fractions, we get

$[\sqrt{729} + \sqrt[3]{0.729} + \sqrt{0.0729}] \times \sqrt{\frac{1}{729}}$

$= [\sqrt{729} + \sqrt[3]{\frac{729}{1000}} + \sqrt{\frac{729}{10000}}] \times \sqrt{\frac{1}{729}}$

Using the properties of square roots and cube roots, we get

$= [\sqrt{729} + \frac{\sqrt[3]{729}}{\sqrt[3]{1000}} + \frac{\sqrt{729}}{\sqrt{10000}}] \times \frac{1}{\sqrt{729}}$

$= [\sqrt{3 \times 3 \times 3 \times 3 \times 3 \times 3} + \frac{\sqrt[3]{3 \times 3 \times 3 \times 3 \times 3 \times 3}}{\sqrt[3]{10 \times 10 \times 10}} + \frac{\sqrt{3 \times 3 \times 3 \times 3 \times 3 \times 3}}{\sqrt{10 \times 10 \times 10 \times 10}}] \times \frac{1}{\sqrt{3 \times 3 \times 3 \times 3 \times 3 \times 3}}$

$= [3 \times 3 \times 3 + \frac{3 \times 3}{10} + \frac{3 \times 3 \times 3}{10 \times 10}] \times \frac{1}{3 \times 3 \times 3}$

$= [27 + \frac{9}{10} + \frac{27}{10 \times 10}] \times \frac{1}{27}$

$= [\frac{2700 + 90 + 27}{100}] \times \frac{1}{27}$

$= \frac{2817}{100} \times \frac{1}{27}$

$= \frac{3 \times 3 \times 313}{100} \times \frac{1}{3 \times 3 \times 3}$

$= \frac{313}{300} = 1.043$

Simplify: $[\sqrt{729} + \sqrt[3]{0.729} + \sqrt{0.0729}] \times \sqrt{\frac{1}{729}}$

Important Questions on Square and Square Root; Cube and Cube Root

Learn and Prepare for any exam you want !

Simplify: 729+0.7293+0.0729×1729

Important Questions on Square and Square Root; Cube and Cube Root

Learn and Prepare for any exam you want !

Simplify: $[\sqrt{729} + \sqrt[3]{0.729} + \sqrt{0.0729}] \times \sqrt{\frac{1}{729}}$