Chapter 8: Q. 90 (page 772)

In the following exercises, use the Quotient Property to simplify square roots.
$a . \sqrt{\frac{121}{16}} b . \sqrt[3]{\frac{16}{250}} c . \sqrt[4]{\frac{32}{162}}$

Short Answer

Expert verified

The simplified expressions are,

$a . \frac{11}{4} b . \frac{2}{5} c . \frac{2}{3}$

Step by step solution

Step 1 Given expressions are,

$a . \sqrt{\frac{121}{16}} b . \sqrt[3]{\frac{16}{250}} c . \sqrt[4]{\frac{32}{162}}$

The objective is, we need to find the simplified expressions for the given expressions.

The quotient property is given by,

$\sqrt[n]{\frac{a}{b}} = \frac{\sqrt[n]{a}}{\sqrt[n]{b}}$ .

Part a Step 2 src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHhtbG5zOndycz0iaHR0cDovL3d3dy53aXJpcy5jb20veG1sL21hdGhtbC1leHRlbnNpb24iIGhlaWdodD0iNDUiIHdpZHRoPSI1MiIgd3JzOmJhc2VsaW5lPSIzMCI+PCEtLU1hdGhNTDogPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtc3FydD48bWZyYWM+PG1uPjEyMTwvbW4+PG1uPjE2PC9tbj48L21mcmFjPjwvbXNxcnQ+PC9tYXRoPi0tPjxkZWZzPjxzdHlsZSB0eXBlPSJ0ZXh0L2NzcyIvPjwvZGVmcz48cG9seWxpbmUgZmlsbD0ibm9uZSIgcG9pbnRzPSIxMiwtMzggMTEsLTM4IDUsMCAyLC0xNSIgc3Ryb2tlPSIjMDAwMDAwIiBzdHJva2UtbGluZWNhcD0ic3F1YXJlIiBzdHJva2Utd2lkdGg9IjEiIHRyYW5zZm9ybT0idHJhbnNsYXRlKDAuNSw0Mi41KSIvPjxwb2x5bGluZSBmaWxsPSJub25lIiBwb2ludHM9IjUsMCAyLC0xNSAwLC0xMyIgc3Ryb2tlPSIjMDAwMDAwIiBzdHJva2UtbGluZWNhcD0ic3F1YXJlIiBzdHJva2Utd2lkdGg9IjEiIHRyYW5zZm9ybT0idHJhbnNsYXRlKDAuNSw0Mi41KSIvPjxsaW5lIHN0cm9rZT0iIzAwMDAwMCIgc3Ryb2tlLWxpbmVjYXA9InNxdWFyZSIgc3Ryb2tlLXdpZHRoPSIxIiB4MT0iMTIuNSIgeDI9IjUwLjUiIHkxPSI0LjUiIHkyPSI0LjUiLz48bGluZSBzdHJva2U9IiMwMDAwMDAiIHN0cm9rZS1saW5lY2FwPSJzcXVhcmUiIHN0cm9rZS13aWR0aD0iMSIgeDE9IjE2LjUiIHgyPSI0Ni41IiB5MT0iMjQuNSIgeTI9IjI0LjUiLz48dGV4dCBmb250LWZhbWlseT0iQXJpYWwiIGZvbnQtc2l6ZT0iMTYiIHRleHQtYW5jaG9yPSJtaWRkbGUiIHg9IjMxLjUiIHk9IjE5Ij4xMjE8L3RleHQ+PHRleHQgZm9udC1mYW1pbHk9IkFyaWFsIiBmb250LXNpemU9IjE2IiB0ZXh0LWFuY2hvcj0ibWlkZGxlIiB4PSIzMi41IiB5PSI0MSI+MTY8L3RleHQ+PC9zdmc+" localid="1645431102703" src="https://studysmarter-mediafiles.s3.amazonaws.com/media/textbook-exercise-images/91920281-5371-48c0-9ac9-ce8d7d48d2d8.svg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIA4OLDUDE42UZHAIET%2F20220223%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20220223T155617Z&X-Amz-Expires=90000&X-Amz-SignedHeaders=host&X-Amz-Signature=3a1d1d96aaf7b0fe15613e4813781ff0195c0f682c85619a994dda3044381caa" src="https://studysmarter-mediafiles.s3.amazonaws.com/media/textbook-exercise-images/91920281-5371-48c0-9ac9-ce8d7d48d2d8.svg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIA4OLDUDE42UZHAIET%2F20220221%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20220221T081319Z&X-Amz-Expires=90000&X-Amz-SignedHeaders=host&X-Amz-Signature=ac08d6dea2a1a1ce2bf82e55a5e76279913877860b97b6c96925e9402dd6e064" 12116.

Now use the quotient property.

$\sqrt{\frac{121}{16}} = \sqrt{\frac{11 \times 11}{4 \times 4}} = \sqrt{\frac{{(11)}^{2}}{{(4)}^{2}}} = \frac{\sqrt{{(11)}^{2}}}{\sqrt{{(4)}^{2}}} = \frac{11}{4}$

Part b Step 2 162503.

$\sqrt[3]{\frac{16}{250}} = \sqrt[3]{\frac{2 \times 8}{2 \times 125}} = \sqrt[3]{\frac{8}{125}}$

Now use the quotient property.

$\sqrt[3]{\frac{16}{250}} = \frac{\sqrt[3]{8}}{\sqrt[3]{125}} = \frac{\sqrt[3]{{(2)}^{3}}}{\sqrt[3]{{(5)}^{3}}} = \frac{2}{5}$

Part c Step 2321624.

$\sqrt[4]{\frac{32}{162}} = \sqrt[4]{\frac{2 \times 16}{2 \times 81}} = \sqrt[4]{\frac{16}{81}}$

Now use the quotient property.

$\sqrt[4]{\frac{32}{162}} = \frac{\sqrt[4]{16}}{\sqrt[4]{81}} = \frac{\sqrt[4]{{(2)}^{4}}}{\sqrt[4]{(3^{4})}} = \frac{2}{3}$

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In the following exercises, use the Quotient Property to simplify square roots.
$a . \sqrt{\frac{121}{16}} b . \sqrt[3]{\frac{16}{250}} c . \sqrt[4]{\frac{32}{162}}$

Short Answer

Step by step solution

Step 1 Given expressions are,

Part b Step 2 162503.

Part c Step 2321624.

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In the following exercises, use the Quotient Property to simplify square roots.a.12116b.162503c.321624

Short Answer

Step by step solution

Step 1 Given expressions are,

Part b Step 2 162503.

Part c Step 2321624.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Statistics

Decision Maths

Applied Mathematics

Pure Maths

Calculus

Study anywhere. Anytime. Across all devices.

In the following exercises, use the Quotient Property to simplify square roots.
$a . \sqrt{\frac{121}{16}} b . \sqrt[3]{\frac{16}{250}} c . \sqrt[4]{\frac{32}{162}}$