/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 146 Suppose you have a calculator th... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 146

Suppose you have a calculator that can only compute square roots. Explain how you could use this calculator to compute \(7^{1 / 8}\).

Short Answer

Expert verified
To compute \(7^{1/8}\) using a calculator with only square root functionality, express \(7^{1/8}\) as a series of square roots: \(((7^{1/8})^{1/2})^{1/2}\). Compute the square root of 7, then take the square root of the result twice. Doing this, we get \(7^{1/8} \approx 1.276055\).

Step by step solution

01

Rewrite the expression as repeated square roots

Express \(7^{1/8}\) as a series of square roots. Notice that since \(8 = 2^3\), the 8th root of 7 can be written as: \[ 7^{1/8} = (7^{1/2})^{1/4} = ((7^{1/8})^{1/2})^{1/2} \]
02

Compute the square root of 7

First, use the calculator to find the square root of 7: \[ \sqrt{7} \approx 2.645751 \]
03

Compute the square root of the previous result

Next, find the square root of the result from Step 2: \[ \sqrt{2.645751} \approx 1.626576 \]
04

Compute the square root of the previous result again

Finally, find the square root of the result from Step 3: \[ \sqrt{1.626576} \approx 1.276055 \]
05

Conclusion

So, using the calculator that can only compute square roots, we find that \(7^{1/8} \approx 1.276055\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Suppose \(p(x)=a_{0}+a_{1} x+\cdots+a_{n} x^{n},\) where \(a_{0}, a_{1}, \ldots, a_{n}\) are integers. Suppose \(M\) and \(N\) are nonzero integers with no common factors and \(\frac{M}{N}\) is a zero of \(p\). Show that \(a_{0} / M\) and \(a_{n} / N\) are integers. [Thus to find rational zeros of a polynomial with integer coefficients, we need only look at fractions whose numerator is a divisor of the constant term and whose denominator is a divisor of the coefficient of highest degree. This result is called the Rational Zeros Theorem or the Rational Roots Theorem.]

Explain why the polynomial \(p\) defined by $$ p(x)=x^{6}+100 x^{2}+5 $$ has no real zeros.

Write the indicated expression as a ratio of polynomials, assuming that $$ r(x)=\frac{3 x+4}{x^{2}+1}, \quad s(x)=\frac{x^{2}+2}{2 x-1}, \quad t(x)=\frac{5}{4 x^{3}+3} $$. $$ (r \circ t)(x) $$

Suppose \(t(x)=\frac{5}{4 x^{3}+3}\). (a) Show that the point (-1,-5) is on the graph of \(t\) (b) Give an estimate for the slope of a line containing (-1,-5) and a point on the graph of \(t\) very close to (-1,-5)

Write the indicated expression as a ratio of polynomials, assuming that $$ r(x)=\frac{3 x+4}{x^{2}+1}, \quad s(x)=\frac{x^{2}+2}{2 x-1}, \quad t(x)=\frac{5}{4 x^{3}+3} $$. $$ (s(x))^{2} t(x) $$
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Applied Mathematics

Read Explanation

Statistics

Read Explanation

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Geometry

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.