# Problem 80: Square root digital expansion

## Solutions

Solution 1 (Click to Show/Hide)
``````function sqrtDigitalExpansion(n) {
function sumDigits(number) {
let sum = 0;
while (number > 0n) {
let digit = number % 10n;
sum += parseInt(digit, 10);
number = number / 10n;
}
return sum;
}

function power(numberA, numberB) {
let result = 1n;
for (let b = 0; b < numberB; b++) {
result = result * BigInt(numberA);
}
return result;
}

// Based on http://www.afjarvis.staff.shef.ac.uk/maths/jarvisspec02.pdf
function expandSquareRoot(number, numDigits) {
let a = 5n * BigInt(number);
let b = 5n;
const boundaryWithNeededDigits = power(10, numDigits + 1);

while (b < boundaryWithNeededDigits) {
if (a >= b) {
a = a - b;
b = b + 10n;
} else {
a = a * 100n;
b = (b / 10n) * 100n + 5n;
}
}
return b / 100n;
}

let result = 0;
let nextPerfectRoot = 1;
const requiredDigits = 100;
for (let i = 1; i <= n; i++) {
if (nextPerfectRoot ** 2 === i) {
nextPerfectRoot++;
continue;
}
result += sumDigits(expandSquareRoot(i, requiredDigits));
}

return result;
}
``````