Simplify Radicals in DESMOS (in Radical Form)

Summary

In this video, Erica, a math tutor, shares a simple Desmos hack for simplifying radicals into radical form. She demonstrates how to solve for a square root (like √320) in radical form using Desmos by creating a table with a specific equation and squaring values. Erica walks viewers through the process of identifying when the decimal approximations stabilize, allowing them to extract the simplified radical expression. By the end, viewers learn how to express square roots in simplified radical form, offering an easy way to convert decimals into exact radical expressions.

Takeaways

• 😀 Erica is a math tutor sharing a hack to simplify radicals in Desmos.
• 😀 The hack helps convert square roots into radical form, not just decimal approximations.
• 😀 Erica demonstrates the process using the square root of 320 as an example.
• 😀 Desmos automatically gives the square root as a decimal, but the goal is to convert it to radical form.
• 😀 To begin, create a table in Desmos by typing 'table' and pressing 'e'.
• 😀 The Y-axis of the table will hold the number under the radical, and the X-axis is used for X squared.
• 😀 To square a number in Desmos, use the carrot symbol (^) by pressing Shift and the key above the 6.
• 😀 Erica suggests filling in the table with a sequence of numbers starting with -21, increasing by 1 each time.
• 😀 The key is to look for the first whole number after a long string of decimals in the table.
• 😀 Once the first whole number is reached (like 5), that number is part of the radical, while the other part stays outside.
• 😀 In the example, the square root of 320 simplifies to 8√5, which matches the decimal approximation.

Q & A

What is the main purpose of the tutorial in the script?

The tutorial demonstrates how to simplify a radical expression into its simplest radical form using a Desmos hack.

What is the specific example used to illustrate the radical simplification process?

The example used is simplifying the square root of 320 into its radical form.

What tool does the tutor recommend using for this process?

The tutor recommends using Desmos, a graphing calculator tool, to perform the radical simplification.

What is the 'hack' mentioned for simplifying radicals?

The hack involves using the table function in Desmos to break down the radical and find the simplified form by analyzing decimal values.

What should you do once you enter the table function in Desmos?

Once you enter the table function, you replace the Y values with the number under the radical sign and divide by X squared, using the carrot symbol (^) to denote squaring.

How do you input squaring in Desmos on the keyboard?

To input squaring in Desmos, you press Shift and the number key that has a carrot symbol (^), usually above the 6 key.

What is the goal when scrolling through the decimals in the Desmos table?

The goal is to continue scrolling through the decimals until you reach the first whole number, which indicates the simplified form of the radical.

How do you determine the simplified radical form of a number from the Desmos table?

You determine the simplified radical form by noting the whole number you reach when scrolling through the decimals, and this number is placed outside the radical. The number under the radical is the remaining part.

What is the simplified radical form of the square root of 320 as shown in the tutorial?

The simplified radical form of the square root of 320 is 8√5.

What does the tutor mean when they refer to 'decimal after decimal after decimal'?

The tutor is referring to the series of decimal values that appear in Desmos as you scroll through the table, eventually leading to a whole number that gives the simplified radical expression.